Noncommutative Geometry and Cayley-smooth Orders - Lieven Le Bruyn

Noncommutative Geometry and Cayley-smooth Orders

(Autor)

Buch | Softcover
592 Seiten
2019
Chapman & Hall/CRC (Verlag)
978-0-367-38870-6 (ISBN)
77,30 inkl. MwSt
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

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

Erscheinungsdatum
Sprache englisch
Maße 156 x 234 mm
Gewicht 453 g
Themenwelt Mathematik / Informatik Mathematik Algebra
Mathematik / Informatik Mathematik Angewandte Mathematik
Mathematik / Informatik Mathematik Arithmetik / Zahlentheorie
Naturwissenschaften Physik / Astronomie
ISBN-10 0-367-38870-7 / 0367388707
ISBN-13 978-0-367-38870-6 / 9780367388706
Zustand Neuware
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