Noncommutative Geometry and Cayley-smooth Orders

ISBN: 9780367388706 出版年：2007 页码：590 Le Bruyn, Lieven CRC Press

Preface Introduction Noncommutative algebra Noncommutative geometry Noncommutative desingularizations Cayley-Hamilton Algebras Conjugacy classes of matrices Simultaneous conjugacy classes Matrix invariants and necklaces The trace algebra The symmetric group Necklace relations Trace relations Cayley-Hamilton algebras Reconstructing Algebras Representation schemes Some algebraic geometry The Hilbert criterium Semisimple modules Some invariant theory Geometric reconstruction The Gerstenhaber-Hesselink theorem The real moment map Etale Technology Etale topology Central simple algebras Spectral sequences Tsen and Tate fields Coniveau spectral sequence The Artin-Mumford exact sequence Normal spaces Knop-Luna slices Quiver Technology Smoothness Local structure Quiver orders Simple roots Indecomposable roots Canonical decomposition General subrepresentations Semistable representations Semisimple Representations Representation types Cayley-smooth locus Reduction steps Curves and surfaces Complex moment map Preprojective algebras Central smooth locus Central singularities Nilpotent Representations Cornering matrices Optimal corners Hesselink stratification Cornering quiver representations Simultaneous conjugacy classes Representation fibers Brauer-Severi varieties Brauer-Severi fibers Noncommutative Manifolds Formal structure Semi-invariants Universal localization Compact manifolds Differential forms deRham cohomology Symplectic structure Necklace Lie algebras Moduli Spaces Moment maps Dynamical systems Deformed preprojective algebras Hilbert schemes Hyper Kahler structure Calogero particles Coadjoint orbits Adelic Grassmannian References Index