Noncommutative Geometry and Cayley-smooth Orders

Lieven Le Bruyn

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Hardback

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English

Chapman & Hall/CRC
24 August 2007

Algebra; Number theory; Mathematical physics

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.

By: Lieven Le Bruyn
Imprint: Chapman & Hall/CRC
Country of Publication: United Kingdom
Volume: 290
Dimensions: Height: 234mm, Width: 156mm, Spine: 38mm
Weight: 929g
ISBN: 9781420064223
ISBN 10: 1420064223
Pages: 588
Publication Date: 24 August 2007
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

Preface. Introduction. Cayley-Hamilton Algebras. Reconstructing Algebras. Étale Technology. Quiver Technology. Semisimple Representations. Nilpotent Representations. Noncommutative Manifolds. Moduli Spaces. References. Index.

Le Bruyn, Lieven