Noncommutative Geometry and Cayley-Smooth Orders

ISBN-13: 9780367388706 / Angielski / Miękka / 2019 / 592 str.

Lieven Le Bruyn

Opis

This book explains the theory of Cayley-smooth orders in central simple algebras over function fields of varieties. 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 contain the main results on Cayley-smooth orders, including semisimple and nilpotent representations. The final chapters study Quillen-smooth algebras via their finite dimensional representations.

Spis treści

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

O autorze

Le Bruyn, Lieven