Lounesto, Pertti
Overview
Works:  19 works in 74 publications in 2 languages and 1,846 library holdings 

Genres:  Conference proceedings 
Roles:  Author, Editor, Other 
Classifications:  QA199, 512.57 
Publication Timeline
.
Most widely held works by
Pertti Lounesto
Clifford algebras and spinors by
Pertti Lounesto(
Book
)
30 editions published between 1997 and 2006 in English and held by 571 WorldCat member libraries worldwide
2. Complex numbers2.1 The field C versus the real algebra C; 2.2 The doublering 2R of R; 2.3 Representation by means of real 2 x 2matrices; 2.4 C as the even Clifford algebra Cl+2; 2.5 Imaginary unit = the unit bivector; 2.6 Even and odd parts; 2.7 Involutions and the norm; 2.8 Vectors multiplied by complex numbers; 2.9 The group Spin(2); Bibliography; 3. Bivectors and the exterior algebra; 3.1 Bivectors as directed plane segments; 3.2 Addition of bivectors; 3.3 Basis of the linear space of bivectors; 3.4 The oriented volume element; 3.5 The cross product; 3.6 The Hodge dual
30 editions published between 1997 and 2006 in English and held by 571 WorldCat member libraries worldwide
2. Complex numbers2.1 The field C versus the real algebra C; 2.2 The doublering 2R of R; 2.3 Representation by means of real 2 x 2matrices; 2.4 C as the even Clifford algebra Cl+2; 2.5 Imaginary unit = the unit bivector; 2.6 Even and odd parts; 2.7 Involutions and the norm; 2.8 Vectors multiplied by complex numbers; 2.9 The group Spin(2); Bibliography; 3. Bivectors and the exterior algebra; 3.1 Bivectors as directed plane segments; 3.2 Addition of bivectors; 3.3 Basis of the linear space of bivectors; 3.4 The oriented volume element; 3.5 The cross product; 3.6 The Hodge dual
Clifford algebras with numeric and symbolic computations by
Rafał Abłamowicz(
Book
)
8 editions published in 1996 in English and held by 210 WorldCat member libraries worldwide
Clifford algebras are at a crossing point in a variety of research areas, including abstract algebra, crystallography, projective geometry, quantum mechanics, differential geometry and analysis. For many researchers working in this field in ma thematics and physics, computer algebra software systems have become indispensable tools in theory and applications. This edited survey book consists of 20 chapters showing application of Clifford algebra in quantum mechanics, field theory, spinor calculations, projective geometry, Hypercomplex algebra, function theory and crystallography. Many examples of computations performed with a variety of readily available software programs are presented in detail, i.e., Maple, Mathematica, Axiom, etc. A key feature of the book is that it shows how scientific knowledge can advance with the use of computational tools and software
8 editions published in 1996 in English and held by 210 WorldCat member libraries worldwide
Clifford algebras are at a crossing point in a variety of research areas, including abstract algebra, crystallography, projective geometry, quantum mechanics, differential geometry and analysis. For many researchers working in this field in ma thematics and physics, computer algebra software systems have become indispensable tools in theory and applications. This edited survey book consists of 20 chapters showing application of Clifford algebra in quantum mechanics, field theory, spinor calculations, projective geometry, Hypercomplex algebra, function theory and crystallography. Many examples of computations performed with a variety of readily available software programs are presented in detail, i.e., Maple, Mathematica, Axiom, etc. A key feature of the book is that it shows how scientific knowledge can advance with the use of computational tools and software
Clifford algebras : applications to mathematics, physics, and engineering by
Rafał Abłamowicz(
Book
)
1 edition published in 2004 in English and held by 128 WorldCat member libraries worldwide
The invited papers in this volume provide a detailed examination of Clifford algebras and their significance to geometry, analysis, physics, and engineering. Divided into five parts, the book's first section is devoted to Clifford analysis; here, topics encompass the Morera problem, inverse scattering associated with the Schrdinger equation, discrete Stokes equations in the plane, a symmetric functional calculus, Poincar series, differential operators in Lipschitz domains, PaleyWiener theorems and Shannon sampling, Bergman projections, and quaternionic calculus for a class of boundary value problems. A careful discussion of geometric applications of Clifford algebras follows, with papers on hyperHermitian manifolds, spin structures and Clifford bundles, differential forms on conformal manifolds, connection and torsion, Casimir elements and Bochner identities on Riemannian manifolds, RaritaSchwinger operators, and the interface between noncommutative geometry and physics. In addition, attention is paid to the algebraic and Lietheoretic applications of Clifford algebrasparticularly their intersection with Hopf algebras, Lie algebras and representations, graded algebras, and associated mathematical structures. Symplectic Clifford algebras are also discussed. Finally, Clifford algebras play a strong role in both physics and engineering. The physics section features an investigation of geometric algebras, chiral Dirac equations, spinors and Fermions, and applications of Clifford algebras in classical mechanics and general relativity. Twistor and octonionic methods, electromagnetism and gravity, elementary particle physics, noncommutative physics, Dirac's equation, quantum spheres, and the Standard Model are among topics considered at length. The section devoted to engineering applications includes papers on twist representations for cycloidal curves, a description of an image space using CayleyKlein geometry, pose estimation, and implementations of Clifford algebra coprocessor design. While the papers collected in this volume require that the reader possess a solid knowledge of appropriate background material, they lead to the most current research topics. With its wide range of topics, wellestablished contributors, and excellent references and index, this book will appeal to graduate students and researchers
1 edition published in 2004 in English and held by 128 WorldCat member libraries worldwide
The invited papers in this volume provide a detailed examination of Clifford algebras and their significance to geometry, analysis, physics, and engineering. Divided into five parts, the book's first section is devoted to Clifford analysis; here, topics encompass the Morera problem, inverse scattering associated with the Schrdinger equation, discrete Stokes equations in the plane, a symmetric functional calculus, Poincar series, differential operators in Lipschitz domains, PaleyWiener theorems and Shannon sampling, Bergman projections, and quaternionic calculus for a class of boundary value problems. A careful discussion of geometric applications of Clifford algebras follows, with papers on hyperHermitian manifolds, spin structures and Clifford bundles, differential forms on conformal manifolds, connection and torsion, Casimir elements and Bochner identities on Riemannian manifolds, RaritaSchwinger operators, and the interface between noncommutative geometry and physics. In addition, attention is paid to the algebraic and Lietheoretic applications of Clifford algebrasparticularly their intersection with Hopf algebras, Lie algebras and representations, graded algebras, and associated mathematical structures. Symplectic Clifford algebras are also discussed. Finally, Clifford algebras play a strong role in both physics and engineering. The physics section features an investigation of geometric algebras, chiral Dirac equations, spinors and Fermions, and applications of Clifford algebras in classical mechanics and general relativity. Twistor and octonionic methods, electromagnetism and gravity, elementary particle physics, noncommutative physics, Dirac's equation, quantum spheres, and the Standard Model are among topics considered at length. The section devoted to engineering applications includes papers on twist representations for cycloidal curves, a description of an image space using CayleyKlein geometry, pose estimation, and implementations of Clifford algebra coprocessor design. While the papers collected in this volume require that the reader possess a solid knowledge of appropriate background material, they lead to the most current research topics. With its wide range of topics, wellestablished contributors, and excellent references and index, this book will appeal to graduate students and researchers
Clifford numbers and spinors : with Riesz's private lectures to E. Folke Bolinder and a historical review by Pertti Lounesto by
Marcel Riesz(
Book
)
7 editions published in 1993 in English and held by 118 WorldCat member libraries worldwide
This volume contains a facsimile reproduction of Marcel Riesz's notes of a set of lectures he delivered at the University of Maryland, College Park, between October 1957 and January 1958, which has not been formally published to date. This seminal material (arranged in four chapters), which contributed greatly to the start of modern research on Clifford algebras, is supplemented in this book by notes which Riesz dictated to E. Folke Bolinder in the following year and which were intended to be a fifth chapter of the Riesz lecture notes. In addition, Riesz's work on Clifford algebra is put into an historical perspective in a separate review by P. Lounesto. As well as providing an introduction to Clifford algebra, this volume will be of value to those interested in the history of mathematics
7 editions published in 1993 in English and held by 118 WorldCat member libraries worldwide
This volume contains a facsimile reproduction of Marcel Riesz's notes of a set of lectures he delivered at the University of Maryland, College Park, between October 1957 and January 1958, which has not been formally published to date. This seminal material (arranged in four chapters), which contributed greatly to the start of modern research on Clifford algebras, is supplemented in this book by notes which Riesz dictated to E. Folke Bolinder in the following year and which were intended to be a fifth chapter of the Riesz lecture notes. In addition, Riesz's work on Clifford algebra is put into an historical perspective in a separate review by P. Lounesto. As well as providing an introduction to Clifford algebra, this volume will be of value to those interested in the history of mathematics
Clifford algebras and spinor structures : a special volume dedicated to the memory of Albert Crumeyrolle, 19191992 by
Rafał Abłamowicz(
Book
)
9 editions published between 1995 and 2011 in English and held by 117 WorldCat member libraries worldwide
This volume introduces mathematicians and physicists to a crossing point of algebra, physics, differential geometry and complex analysis. The book follows the French tradition of Cartan, Chevalley and Crumeyrolle and summarizes Crumeyrolle's own work on exterior algebra and spinor structures. The depth and breadth of Crumeyrolle's research interests and influence in the field is investigated in a number of articles. Of interest to physicists is the modern presentation of Crumeyrolle's approach to Weyl spinors, and to his spinoriality groups, which are formulated with spinor operators of Kustaanheimo and Hestenes. The Dirac equation and Dirac operator are studied both from the complex analytic and differential geometric points of view, in the modern sense of Ryan and Trautman. For mathematicians and mathematical physicists whose research involves algebra, quantum mechanics and differential geometry
9 editions published between 1995 and 2011 in English and held by 117 WorldCat member libraries worldwide
This volume introduces mathematicians and physicists to a crossing point of algebra, physics, differential geometry and complex analysis. The book follows the French tradition of Cartan, Chevalley and Crumeyrolle and summarizes Crumeyrolle's own work on exterior algebra and spinor structures. The depth and breadth of Crumeyrolle's research interests and influence in the field is investigated in a number of articles. Of interest to physicists is the modern presentation of Crumeyrolle's approach to Weyl spinors, and to his spinoriality groups, which are formulated with spinor operators of Kustaanheimo and Hestenes. The Dirac equation and Dirac operator are studied both from the complex analytic and differential geometric points of view, in the modern sense of Ryan and Trautman. For mathematicians and mathematical physicists whose research involves algebra, quantum mechanics and differential geometry
Spinor valued regular functions in hypercomplex analysis by
Pertti Lounesto(
Book
)
4 editions published in 1979 in English and Undetermined and held by 6 WorldCat member libraries worldwide
4 editions published in 1979 in English and Undetermined and held by 6 WorldCat member libraries worldwide
Clifford numbers and spinors : with Riesz's private lectures to E. Folke Bolinder and a historical review by
Marcel Riesz(
Book
)
1 edition published in 2011 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2011 in English and held by 2 WorldCat member libraries worldwide
Covariances of the Maxwell and Dirac equation by Kennett Aschan(
Book
)
1 edition published in 2001 in English and held by 1 WorldCat member library worldwide
1 edition published in 2001 in English and held by 1 WorldCat member library worldwide
Conformal transformations and Clifford algebras by
Pertti Lounesto(
Book
)
1 edition published in 1978 in English and held by 1 WorldCat member library worldwide
1 edition published in 1978 in English and held by 1 WorldCat member library worldwide
On left ideals of Clifford algebras by Esko Latvamaa(
Book
)
1 edition published in 1979 in English and held by 1 WorldCat member library worldwide
1 edition published in 1979 in English and held by 1 WorldCat member library worldwide
CLICAL user manual : version 2.0, complex number, vector space and Clifford algebra calculator for MSDOS personal computers by
Pertti Lounesto(
Book
)
2 editions published in 1987 in English and held by 1 WorldCat member library worldwide
2 editions published in 1987 in English and held by 1 WorldCat member library worldwide
Clifford algebras and potential theory : proceedings of the Summer School held in Mekrijärvi, June 2428, 2002 by Summer School on Clifford Algebras and Potential Theory(
Book
)
1 edition published in 2004 in English and held by 1 WorldCat member library worldwide
1 edition published in 2004 in English and held by 1 WorldCat member library worldwide
On primitive idempotents of Clifford algebras by
Pertti Lounesto(
Book
)
1 edition published in 1977 in English and held by 1 WorldCat member library worldwide
1 edition published in 1977 in English and held by 1 WorldCat member library worldwide
Lie groups of motor integrals of generalized Kepler motion by
Pertti Lounesto(
Book
)
1 edition published in 1977 in English and held by 1 WorldCat member library worldwide
1 edition published in 1977 in English and held by 1 WorldCat member library worldwide
Spinors and BrauerWall groups by
Pertti Lounesto(
Book
)
1 edition published in 1978 in English and held by 1 WorldCat member library worldwide
1 edition published in 1978 in English and held by 1 WorldCat member library worldwide
Differentiaalimuodot sähkömagnetiikassa by
Ismo V Lindell(
Book
)
1 edition published in 1995 in Finnish and held by 1 WorldCat member library worldwide
1 edition published in 1995 in Finnish and held by 1 WorldCat member library worldwide
CLICAL: complex number, vector space and Clifford algebra calculator for MSDOS personal computers : user manual (version
2.0) by
Pertti Lounesto(
Book
)
1 edition published in 1987 in English and held by 1 WorldCat member library worldwide
1 edition published in 1987 in English and held by 1 WorldCat member library worldwide
CLICAL, version 2.0 : complex number, vector space and Clifford algebra calculator for MSDOS personal computers ; user manual by
Pertti Lounesto(
Book
)
1 edition published in 1987 in English and held by 1 WorldCat member library worldwide
1 edition published in 1987 in English and held by 1 WorldCat member library worldwide
Lectures on Clifford (geometric) algebras and applications by
Rafał Abłamowicz(
)
2 editions published in 2004 in English and held by 0 WorldCat member libraries worldwide
The subject of Clifford (geometric) algebras offers a unified algebraic framework for the direct expression of the geometric concepts underlying the mathematical theories of linear and multilinear algebra, projective and affine geometries, and differential geometry. This bird'seye view of Clifford (geometric) algebras and their applications is presented by six of the world's leading experts in the field. Key topics and features of this systematic exposition: * An Introductory chapter on Clifford Algebras by Pertti Lounesto * Ian Porteous (Chapter 2) reveals the mathematical structure of Clifford algebras in terms of the classical groups * John Ryan (Chapter 3) introduces the basic concepts of Clifford analysis, which extends the wellknown complex analysis of the plane to three and higher dimensions * William Baylis (Chapter 4) investigates some of the extensive applications that have been made in mathematical physics, including the basic ideas of electromagnetism and special relativity * John Selig (Chapter 5) explores the successes that Clifford algebras, especially quaternions and biquaternions, have found in computer vision and robotics * Tom Branson (Chapter 6) discusses some of the deepest results that Clifford algebras have made possible in our understanding of differential geometry * Editors (Appendix) give an extensive review of various software packages for computations with Clifford algebras including standalone programs, online calculators, special purpose numeric software, and symbolic addons to computer algebra systems This text will serve beginning graduate students and researchers in diverse areasmathematics, physics, computer science and engineering; it will be useful both for newcomers who have little prior knowledge of the subject and established professionals who wish to keep abreast of the latest applications
2 editions published in 2004 in English and held by 0 WorldCat member libraries worldwide
The subject of Clifford (geometric) algebras offers a unified algebraic framework for the direct expression of the geometric concepts underlying the mathematical theories of linear and multilinear algebra, projective and affine geometries, and differential geometry. This bird'seye view of Clifford (geometric) algebras and their applications is presented by six of the world's leading experts in the field. Key topics and features of this systematic exposition: * An Introductory chapter on Clifford Algebras by Pertti Lounesto * Ian Porteous (Chapter 2) reveals the mathematical structure of Clifford algebras in terms of the classical groups * John Ryan (Chapter 3) introduces the basic concepts of Clifford analysis, which extends the wellknown complex analysis of the plane to three and higher dimensions * William Baylis (Chapter 4) investigates some of the extensive applications that have been made in mathematical physics, including the basic ideas of electromagnetism and special relativity * John Selig (Chapter 5) explores the successes that Clifford algebras, especially quaternions and biquaternions, have found in computer vision and robotics * Tom Branson (Chapter 6) discusses some of the deepest results that Clifford algebras have made possible in our understanding of differential geometry * Editors (Appendix) give an extensive review of various software packages for computations with Clifford algebras including standalone programs, online calculators, special purpose numeric software, and symbolic addons to computer algebra systems This text will serve beginning graduate students and researchers in diverse areasmathematics, physics, computer science and engineering; it will be useful both for newcomers who have little prior knowledge of the subject and established professionals who wish to keep abreast of the latest applications
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fewer
Audience Level
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Kids  General  Special 
Related Identities
 Abłamowicz, Rafał Author Editor
 Parra, Josep M. 1952 Editor
 Riesz, Marcel 1886 Author
 Crumeyrolle, A. (Albert)
 Bolinder, E. Folke Other Editor
 Baylis, William E.
 Porteous, Ian
 Ryan, John
 Selig, J. M.
 Sobczyk, Garret Editor
Associated Subjects
Algebra Clifford algebras Computer science Computer scienceMathematics Computer software Crumeyrolle, A.(Albert) Engineering mathematics Functions of complex variables Geometry, Differential Global analysis (Mathematics) Global differential geometry Group theory Mathematical physics Mathematics Numerical analysis Potential theory (Mathematics) Quantum theory Spinor analysis Vector algebraData processing