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Noncommutative geometry and Cayley-smooth orders

Author: Lieven Le Bruyn
Publisher: Boca Raton : Chapman & Hall/CRC, ©2008.
Series: Monographs and textbooks in pure and applied mathematics, 290.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

Explains the theory of Cayley-smooth orders in central simple algebras over function fields of varieties. This book describes the etale local structure of such orders as well as their central  Read more...

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Additional Physical Format: Online version:
Le Bruyn, Lieven, 1958-
Noncommutative geometry and Cayley-smooth orders.
Boca Raton : Chapman & Hall/CRC, ©2008
(OCoLC)989861388
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Lieven Le Bruyn
ISBN: 9781420064223 1420064223
OCLC Number: 132582952
Description: lxiii, 524 pages : illustrations ; 25 cm.
Contents: I.1 Noncommutative algebra xvii --
I.2 Noncommutative geometry xxxv --
I.3 Noncommutative desingularizations 1 --
1 Cayley-Hamilton Algebras 1 --
1.1 Conjugacy classes of matrices 1 --
1.2 Simultaneous conjugacy classes 14 --
1.3 Matrix invariants and necklaces 18 --
1.4 The trace algebra 25 --
1.5 The symmetric group 30 --
1.6 Necklace relations 33 --
1.7 Trace relations 42 --
1.8 Cayley-Hamilton algebras 47 --
2 Reconstructing Algebras 55 --
2.1 Representation schemes 55 --
2.2 Some algebraic geometry 58 --
2.3 The Hilbert criterium 64 --
2.4 Semisimple modules 69 --
2.5 Some invariant theory 75 --
2.6 Geometric reconstruction 82 --
2.7 The Gerstenhaber-Hesselink theorem 89 --
2.8 The real moment map 99 --
3 Etale Technology 109 --
3.1 Etale topology 109 --
3.2 Central simple algebras 119 --
3.3 Spectral sequences 123 --
3.4 Tsen and Tate fields 127 --
3.5 Coniveau spectral sequence 132 --
3.6 The Artin-Mumford exact sequence 136 --
3.7 Normal spaces 145 --
3.8 Knop-Luna slices 155 --
4 Quiver Technology 163 --
4.1 Smoothness 163 --
4.2 Local structure 174 --
4.3 Quiver orders 185 --
4.4 Simple roots 197 --
4.5 Indecomposable roots 203 --
4.6 Canonical decomposition 213 --
4.7 General subrepresentations 226 --
4.8 Semistable representations 231 --
5 Semisimple Representations 241 --
5.1 Representation types 241 --
5.2 Cayley-smooth locus 249 --
5.3 Reduction steps 258 --
5.4 Curves and surfaces 271 --
5.5 Complex moment map 285 --
5.6 Preprojective algebras 291 --
5.7 Central smooth locus 294 --
5.8 Central singularities 304 --
6 Nilpotent Representations 315 --
6.1 Cornering matrices 315 --
6.2 Optimal corners 322 --
6.3 Hesselink stratification 326 --
6.4 Cornering quiver representations 335 --
6.5 Simultaneous conjugacy classes 342 --
6.6 Representation fibers 350 --
6.7 Brauer-Severi varieties 362 --
6.8 Brauer-Severi fibers 368 --
7 Noncommutative Manifolds 377 --
7.1 Formal structure 377 --
7.2 Semi-invariants 385 --
7.3 Universal localization 396 --
7.4 Compact manifolds 404 --
7.5 Differential forms 413 --
7.6 deRham cohomology 429 --
7.7 Symplectic structure 438 --
7.8 Necklace Lie algebras 445 --
8 Moduli Spaces 451 --
8.1 Moment maps 452 --
8.2 Dynamical systems 456 --
8.3 Deformed preprojective algebras 464 --
8.4 Hilbert schemes 469 --
8.5 Hyper Kahler structure 482 --
8.6 Calogero particles 487 --
8.7 Coadjoint orbits 493 --
8.8 Adelic Grassmannian 497.
Series Title: Monographs and textbooks in pure and applied mathematics, 290.
Responsibility: Lieven Le Bruyn.
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