Broué, Michel
Overview
Works:  27 works in 94 publications in 4 languages and 1,399 library holdings 

Genres:  Conference papers and proceedings Textbooks 
Roles:  Author, Author of introduction, Contributor 
Classifications:  QA177, 510 
Publication Timeline
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Most widely held works by
Michel Broué
Introduction to complex reflection groups and their braid groups by
Michel Broué(
Book
)
17 editions published in 2010 in English and Undetermined and held by 216 WorldCat member libraries worldwide
"Weyl groups are particular cases of complex reflection groups, i.e. finite subgroups of GLr(C) generated by (pseudo)reflections. These are groups whose polynomial ring of invariants is a polynomial algebra." "It has recently been discovered that complex reflection groups play a key role in the theory of finite reductive groups, giving rise as they do to braid groups and generalized Hecke algebras which govern the representation theory of finite reductive groups. It is now also broadly agreed upon that many of the known properties of Weyl groups can be generalized to complex reflection groups. The purpose of this work is to present a fairly extensive treatment of many basic properties of complex reflection groups (characterization, Steinberg theorem, GutkinOpdam matrices, Solomon theorem and applications, etc.) including the basic findings of Springer theory on eigenspaces. In doing so, we also introduce basic definitions and properties of the associated braid groups, as well as a quick introduction to Bessis' lifting of Springer theory to braid groups."Jacket
17 editions published in 2010 in English and Undetermined and held by 216 WorldCat member libraries worldwide
"Weyl groups are particular cases of complex reflection groups, i.e. finite subgroups of GLr(C) generated by (pseudo)reflections. These are groups whose polynomial ring of invariants is a polynomial algebra." "It has recently been discovered that complex reflection groups play a key role in the theory of finite reductive groups, giving rise as they do to braid groups and generalized Hecke algebras which govern the representation theory of finite reductive groups. It is now also broadly agreed upon that many of the known properties of Weyl groups can be generalized to complex reflection groups. The purpose of this work is to present a fairly extensive treatment of many basic properties of complex reflection groups (characterization, Steinberg theorem, GutkinOpdam matrices, Solomon theorem and applications, etc.) including the basic findings of Springer theory on eigenspaces. In doing so, we also introduce basic definitions and properties of the associated braid groups, as well as a quick introduction to Bessis' lifting of Springer theory to braid groups."Jacket
Représentations unipotentes génériques et blocs des groupes réductifs finis by
Michel Broué(
Book
)
16 editions published in 1993 in 5 languages and held by 163 WorldCat member libraries worldwide
16 editions published in 1993 in 5 languages and held by 163 WorldCat member libraries worldwide
Split spetses for primitive reflection groups by
Michel Broué(
Book
)
7 editions published in 2014 in English and held by 156 WorldCat member libraries worldwide
7 editions published in 2014 in English and held by 156 WorldCat member libraries worldwide
Some topics in algebra : an advanced undergraduate course at PKU by
Michel Broué(
Book
)
13 editions published between 2013 and 2016 in English and held by 29 WorldCat member libraries worldwide
During the springs of 2011 and 2012, the author was invited by Peking University to give an advanced undergraduate algebra course (once a week over two months each year). This book was written during and for that course. By no way does it claim to be to exhaustive. It was originally intended as a brief introduction to algebra for an extremely pleasant and passionate audience. It certainly reflects some of the author's own tastes, and it was influenced by the feelings and the reactions of the students. Nevertheless, the result covers some advanced undergraduate algebra (rings, ideals, basics of fields theory, algebraic integers, modules, hom and tensor functors, projective modules, etc.) illustrated by numerous examples, counterexamples and exercises. Following a worldwide tradition, the author had planned to conclude by lecturing on the structure of finitely generated modules over principal ideal domains. But during the course, after explaining that the notion of projective modules is more natural than the notion of free modules, it became clear that principal ideal domains needed to be replaced by Dedekind rings; this is much less traditional in the literaturebut not more difficult
13 editions published between 2013 and 2016 in English and held by 29 WorldCat member libraries worldwide
During the springs of 2011 and 2012, the author was invited by Peking University to give an advanced undergraduate algebra course (once a week over two months each year). This book was written during and for that course. By no way does it claim to be to exhaustive. It was originally intended as a brief introduction to algebra for an extremely pleasant and passionate audience. It certainly reflects some of the author's own tastes, and it was influenced by the feelings and the reactions of the students. Nevertheless, the result covers some advanced undergraduate algebra (rings, ideals, basics of fields theory, algebraic integers, modules, hom and tensor functors, projective modules, etc.) illustrated by numerous examples, counterexamples and exercises. Following a worldwide tradition, the author had planned to conclude by lecturing on the structure of finitely generated modules over principal ideal domains. But during the course, after explaining that the notion of projective modules is more natural than the notion of free modules, it became clear that principal ideal domains needed to be replaced by Dedekind rings; this is much less traditional in the literaturebut not more difficult
L'affaire Pliouchtch by
JeanJacques Marie(
Book
)
5 editions published in 1976 in French and held by 29 WorldCat member libraries worldwide
5 editions published in 1976 in French and held by 29 WorldCat member libraries worldwide
Séminaire sur les groupes finis by
Equipe de la théorie des groupes finis (Paris)(
Book
)
3 editions published between 1979 and 1983 in French and held by 12 WorldCat member libraries worldwide
3 editions published between 1979 and 1983 in French and held by 12 WorldCat member libraries worldwide
Towards spetses by
Michel Broué(
Book
)
6 editions published in 1999 in English and German and held by 9 WorldCat member libraries worldwide
6 editions published in 1999 in English and German and held by 9 WorldCat member libraries worldwide
On complex reflection groups and their associated braid groups by
Michel Broué(
Book
)
3 editions published in 1994 in English and German and held by 6 WorldCat member libraries worldwide
3 editions published in 1994 in English and German and held by 6 WorldCat member libraries worldwide
Complex reflection groups, braid groups, Hecke algebras by
Michel Broué(
Book
)
2 editions published in 1997 in English and held by 6 WorldCat member libraries worldwide
2 editions published in 1997 in English and held by 6 WorldCat member libraries worldwide
Closed orbits in homology classes by Atsushi Katsuda(
Book
)
1 edition published in 1990 in French and held by 5 WorldCat member libraries worldwide
1 edition published in 1990 in French and held by 5 WorldCat member libraries worldwide
Zyklotomische Heckealgebren by
Michel Broué(
Book
)
3 editions published in 1993 in German and held by 5 WorldCat member libraries worldwide
3 editions published in 1993 in German and held by 5 WorldCat member libraries worldwide
Generalized Harish Chandra theory by
Michel Broué(
Book
)
2 editions published in 1997 in English and held by 5 WorldCat member libraries worldwide
2 editions published in 1997 in English and held by 5 WorldCat member libraries worldwide
Le Réseau de Leech et le groupe de Conway by
Michel Broué(
Book
)
1 edition published in 1970 in French and held by 4 WorldCat member libraries worldwide
1 edition published in 1970 in French and held by 4 WorldCat member libraries worldwide
ISOMETRIES PARFAITES DANS LES GROUPES FINIS by
Raphaël Rouquier(
Book
)
1 edition published in 1992 in French and held by 2 WorldCat member libraries worldwide
SUIVANT M. BROUE, NOUS ETUDIONS CERTAINES ISOMETRIES ENTRE GROUPES DE GROTHENDIECK DE BLOCS A DEFAUT ABELIEN DE GROUPES SYMETRIQUES ET SPORADIQUES, QUI COMMUTENT AVEC LES APPLICATIONS DE DECOMPOSITION GENERALISEES
1 edition published in 1992 in French and held by 2 WorldCat member libraries worldwide
SUIVANT M. BROUE, NOUS ETUDIONS CERTAINES ISOMETRIES ENTRE GROUPES DE GROTHENDIECK DE BLOCS A DEFAUT ABELIEN DE GROUPES SYMETRIQUES ET SPORADIQUES, QUI COMMUTENT AVEC LES APPLICATIONS DE DECOMPOSITION GENERALISEES
Algébre des invariants relatifs pour les groupes de réflexions catégorie stable by
Vincent Beck(
Book
)
1 edition published in 2008 in French and held by 2 WorldCat member libraries worldwide
This thesis consists in two independant parts and an appendix. The first part deals with reflection groups whereas the second part is about stable category. The appendix treats sign rules in categories of complexes. In the first part, we consider a group G acting on the vector space V as a reflection group. We then study the isotypic component relatively to a onedimensional character of G of the following algebra : the tensor product of the symmetric algebra of the dual of V and the exterior algebra of a finite dimensional representation of G. We construct an algebra structure on this isotypic component. We then show that the algebra structure is in fact an exterior algebra structure. The first parts ends with concrete examples. In the second part, we suggest a generalization for a theorem of Rickard. Let M be a functor with right and left adjoint, we define the notion of an Mstable category of an abelian or a triangulated category. The Mstable category is in fact a triangulated category. Moreover in the abelian case, the Mstable category is a quotient of an Mderived category
1 edition published in 2008 in French and held by 2 WorldCat member libraries worldwide
This thesis consists in two independant parts and an appendix. The first part deals with reflection groups whereas the second part is about stable category. The appendix treats sign rules in categories of complexes. In the first part, we consider a group G acting on the vector space V as a reflection group. We then study the isotypic component relatively to a onedimensional character of G of the following algebra : the tensor product of the symmetric algebra of the dual of V and the exterior algebra of a finite dimensional representation of G. We construct an algebra structure on this isotypic component. We then show that the algebra structure is in fact an exterior algebra structure. The first parts ends with concrete examples. In the second part, we suggest a generalization for a theorem of Rickard. Let M be a functor with right and left adjoint, we define the notion of an Mstable category of an abelian or a triangulated category. The Mstable category is in fact a triangulated category. Moreover in the abelian case, the Mstable category is a quotient of an Mderived category
SUR LES GROUPES DE REFLEXIONS COMPLEXES by
DAVID BESSIS(
Book
)
1 edition published in 1998 in French and held by 2 WorldCat member libraries worldwide
CETTE THESE SE COMPOSE DE TROIS PARTIES INDEPENDANTES. DANS LA PREMIERE PARTIE, ON S'INTERESSE A LA SITUATION SUIVANTE. SOIT W UN GROUPE DE REFLEXIONS COMPLEXE, SOIT W UN ELEMENT REGULIER (AU SENS DE SPRINGER) DE W. ON NOTE W(W) LE CENTRALISATEUR DE W DANS W. A W ET W(W), ON PEUT ASSOCIER DES GROUPES DES TRESSES GENERALISES, NOTES RESPECTIVEMENT B ET B(W). REPONDANT A UNE QUESTION SOULEVEE PAR BROUEMICHEL, LE THEOREME PRINCIPAL ETABLIT, SAUF DANS QUELQUES CAS, L'INJECTIVITE DU MORPHISME NATUREL DE B(W) VERS B. LA PREUVE DONNEE CONSISTE A SE RAMENER AU CAS DU GROUPE DES TRESSES D'ARTIN ET A UTILISER UN LEMME (DU INITIALEMENT A ARTIN MAIS APPAREMMENT OUBLIE DEPUIS) SUR LES HOMOTOPIES ENTRE TRESSES USUELLES. ON MET EGALEMENT EN VALEUR LE ROLE DU CHOIX DU POINT BASE ET DES GENERATEURS STANDARDS. LA SECONDE PARTIE EST ISSUE D'UN TRAVAIL COMMUN AVEC CEDRIC BONNAFE ET RAPHAEL ROUQUIER. IL S'AGIT D'EXPLIQUER, PAR LA THEORIE DES INVARIANTS, CERTAINS MORPHISMES DE DIAGRAMMES QUE L'ON PEUT OBSERVER SUR DES TABLES DUES A BROUEMALLEROUQUIER. ON DONNE DES CONDITIONS D'EXISTENCE DE SUITES EXACTES, PAR LESQUELLES CERTAINS GROUPES DE REFLEXIONS APPARAISSENT COMME EXTENSIONS D'AUTRES GROUPES DE REFLEXIONS PAR DES GROUPES D'INTERSECTION COMPLETE. COMME APPLICATION, ON DONNE DE NOUVELLES PRESENTATIONS POUR CERTAINS GROUPES. LA CONSTRUCTION ECLAIRE LA CLASSIFICATION DE SHEPHARDTODD, ET DEVRAIT S'ETENDRE AUX GROUPES DES TRESSES. LA DERNIERE PARTIE A DEJA PARU DANS COMMUNICATIONS IN ALGEBRA. IL S'AGIT DE MONTRER QUE, SI W EST UN GROUPE DE REFLEXIONS COMPLEXES ET SI K EST LE PLUS PETIT CORPS CONTENANT LES VALEURS DU CARACTERES DE LA REPRESENTATION NATURELLE DE W, ALORS TOUS LES CARACTERES DE W SONT RATIONNELS SUR K. CE RESULTAT POURRAIT SE DEDUIRE D'UN RESULTAT DE BENARD SUR LES INDICES DE SCHUR. MAIS COMME LA PREUVE DE BENARD REPOSE EN PARTIE SUR DES TABLES DE CARACTERES ERRONEES, ON A PREFERE DONNER UNE PREUVE INDEPENDANTE, OU LES CALCULS NECESSAIRES SONT EFFECTUES SOUS GAP
1 edition published in 1998 in French and held by 2 WorldCat member libraries worldwide
CETTE THESE SE COMPOSE DE TROIS PARTIES INDEPENDANTES. DANS LA PREMIERE PARTIE, ON S'INTERESSE A LA SITUATION SUIVANTE. SOIT W UN GROUPE DE REFLEXIONS COMPLEXE, SOIT W UN ELEMENT REGULIER (AU SENS DE SPRINGER) DE W. ON NOTE W(W) LE CENTRALISATEUR DE W DANS W. A W ET W(W), ON PEUT ASSOCIER DES GROUPES DES TRESSES GENERALISES, NOTES RESPECTIVEMENT B ET B(W). REPONDANT A UNE QUESTION SOULEVEE PAR BROUEMICHEL, LE THEOREME PRINCIPAL ETABLIT, SAUF DANS QUELQUES CAS, L'INJECTIVITE DU MORPHISME NATUREL DE B(W) VERS B. LA PREUVE DONNEE CONSISTE A SE RAMENER AU CAS DU GROUPE DES TRESSES D'ARTIN ET A UTILISER UN LEMME (DU INITIALEMENT A ARTIN MAIS APPAREMMENT OUBLIE DEPUIS) SUR LES HOMOTOPIES ENTRE TRESSES USUELLES. ON MET EGALEMENT EN VALEUR LE ROLE DU CHOIX DU POINT BASE ET DES GENERATEURS STANDARDS. LA SECONDE PARTIE EST ISSUE D'UN TRAVAIL COMMUN AVEC CEDRIC BONNAFE ET RAPHAEL ROUQUIER. IL S'AGIT D'EXPLIQUER, PAR LA THEORIE DES INVARIANTS, CERTAINS MORPHISMES DE DIAGRAMMES QUE L'ON PEUT OBSERVER SUR DES TABLES DUES A BROUEMALLEROUQUIER. ON DONNE DES CONDITIONS D'EXISTENCE DE SUITES EXACTES, PAR LESQUELLES CERTAINS GROUPES DE REFLEXIONS APPARAISSENT COMME EXTENSIONS D'AUTRES GROUPES DE REFLEXIONS PAR DES GROUPES D'INTERSECTION COMPLETE. COMME APPLICATION, ON DONNE DE NOUVELLES PRESENTATIONS POUR CERTAINS GROUPES. LA CONSTRUCTION ECLAIRE LA CLASSIFICATION DE SHEPHARDTODD, ET DEVRAIT S'ETENDRE AUX GROUPES DES TRESSES. LA DERNIERE PARTIE A DEJA PARU DANS COMMUNICATIONS IN ALGEBRA. IL S'AGIT DE MONTRER QUE, SI W EST UN GROUPE DE REFLEXIONS COMPLEXES ET SI K EST LE PLUS PETIT CORPS CONTENANT LES VALEURS DU CARACTERES DE LA REPRESENTATION NATURELLE DE W, ALORS TOUS LES CARACTERES DE W SONT RATIONNELS SUR K. CE RESULTAT POURRAIT SE DEDUIRE D'UN RESULTAT DE BENARD SUR LES INDICES DE SCHUR. MAIS COMME LA PREUVE DE BENARD REPOSE EN PARTIE SUR DES TABLES DE CARACTERES ERRONEES, ON A PREFERE DONNER UNE PREUVE INDEPENDANTE, OU LES CALCULS NECESSAIRES SONT EFFECTUES SOUS GAP
On the cyclotomic Hecke algebras of complex reflection groups by
Maria Chlouveraki(
Book
)
1 edition published in 2007 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2007 in English and held by 2 WorldCat member libraries worldwide
Des lois du mariage à Bourbaki conférence du mercredi 17 mars 2010(
Visual
)
1 edition published in 2010 in French and held by 1 WorldCat member library worldwide
1 edition published in 2010 in French and held by 1 WorldCat member library worldwide
Special issue in celebration of Claudio Procesi's 60th birthday(
Book
)
1 edition published in 2002 in English and held by 1 WorldCat member library worldwide
1 edition published in 2002 in English and held by 1 WorldCat member library worldwide
Some topics in algebra by
Michel Broué(
Book
)
1 edition published in 2016 in English and held by 1 WorldCat member library worldwide
1 edition published in 2016 in English and held by 1 WorldCat member library worldwide
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Related Identities
 Malle, Gunter
 Michel, Jean
 Mathon, Tania Editor
 Marie, JeanJacques 1937 ... Author Editor
 Cartan, Henri 19042008 Author of introduction
 Schwartz, Laurent 19152002 Author of introduction
 Khodorovitch, Tat'iana Sergeievna Editor
 Comité international des mathématiciens pour la défense de Chikhanovitch et de Pliouchtch (Paris) Editor
 Hée, JeanYves
 Enguehard, Michel
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Associated Subjects
Algebra Algebraic topology Blocks (Group theory) Braid theory Characters of groups Finite groups Galois theory Group algebras Group theory Hecke algebras Homology theory Intellectual life Linear algebraic groups Mathematics Plyushch, Leonid, Political prisoners Psychiatric hospitals Reflection groups Representations of groups Soviet Union Weyl groups