Noncommutative Geometry and Cayley-smooth Orders
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A(C)tale topology
A01=Lieven Le Bruyn
advanced algebraic structures
Affine Variety
Algebra Morphism
algebraic geometry
Author_Lieven Le Bruyn
Azumaya Algebra
BB BB
Category=PBF
Category=PBH
Category=PBW
Category=PHU
Central Simple Algebras
class
Coadjoint Orbit
conjugacy
Conjugacy Classes
De Rham Cohomology
diagram
Dim Rep?
Dim Repα
Dimension Vector
Discrete Valuation Ring
eq_bestseller
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
eq_non-fiction
eq_science
GG GG
Indecomposable Representations
irreducible
isomorphism
Left Exact Functor
Lie Algebra
Moduli Space
noncommutative algebra
ooo
open
Oriented Cycles
partial desingularization
Poisson Algebra
Preprojective Algebra
Quiver Representations
quiver technology
representation theory
Sn C1
Spectral Sequence
Stabilizer Subgroup
subset
Type S1
Witness Algebra
young
zariski
Product details
- ISBN 9781420064223
- Weight: 929g
- Dimensions: 156 x 234mm
- Publication Date: 24 Aug 2007
- Publisher: Taylor & Francis Ltd
- Publication City/Country: GB
- Product Form: Hardback
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Noncommutative Geometry and Cayley-smooth Orders explains the theory of Cayley-smooth orders in central simple algebras over function fields of varieties. In particular, the book describes the étale local structure of such orders as well as their central singularities and finite dimensional representations.
After an introduction to partial desingularizations of commutative singularities from noncommutative algebras, the book presents the invariant theoretic description of orders and their centers. It proceeds to introduce étale topology and its use in noncommutative algebra as well as to collect the necessary material on representations of quivers. The subsequent chapters explain the étale local structure of a Cayley-smooth order in a semisimple representation, classify the associated central singularity to smooth equivalence, describe the nullcone of these marked quiver representations, and relate them to the study of all isomorphism classes of n-dimensional representations of a Cayley-smooth order. The final chapters study Quillen-smooth algebras via their finite dimensional representations.
Noncommutative Geometry and Cayley-smooth Orders provides a gentle introduction to one of mathematics' and physics' hottest topics.
Le Bruyn, Lieven
