Quadratic Algebras

Quadratic Algebras

by A. Polishchuk, Leonid Positselski
     
 

ISBN-10: 0821838342

ISBN-13: 9780821838341

Pub. Date: 12/28/2005

Publisher: American Mathematical Society

Quadratic algebras, i.e., algebras defined by quadratic relations, often occur in various areas of mathematics. One of the main problems in the study of these (and similarly defined) algebras is how to control their size. A central notion in solving this problem is the notion of a Koszul algebra, which was introduced in 1970 by S. Priddy and then appeared in many

Overview

Quadratic algebras, i.e., algebras defined by quadratic relations, often occur in various areas of mathematics. One of the main problems in the study of these (and similarly defined) algebras is how to control their size. A central notion in solving this problem is the notion of a Koszul algebra, which was introduced in 1970 by S. Priddy and then appeared in many areas of mathematics, such as algebraic geometry, representation theory, noncommutative geometry, $K$-theory, number theory, and noncommutative linear algebra. The book offers a coherent exposition of the theory of quadratic and Koszul algebras, including various definitions of Koszulness, duality theory, Poincaré-Birkhoff-Witt-type theorems for Koszul algebras, and the Koszul deformation principle. In the concluding chapter of the book, they explain a surprising connection between Koszul algebras and one-dependent discrete-time stochastic processes.

Product Details

ISBN-13:
9780821838341
Publisher:
American Mathematical Society
Publication date:
12/28/2005
Series:
University Lecture Series, #37
Pages:
159
Product dimensions:
6.80(w) x 9.90(h) x 0.40(d)

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