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Quadratic Algebras
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Quadratic Algebras

Quadratic Algebras

Volume 37

Alexander Polishchuk, Leonid Positselski - Collection University Lecture Series

176 pages, parution le 28/02/2006

Résumé

This book introduces recent developments in the study of algebras defined by quadratic relations. 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 authors give 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.

The book can be used by graduate students and researchers working in algebra and any of the above-mentioned areas of mathematics.

Readership : Graduate students and research mathematicians interested in algebra.

L'auteur - Leonid Positselski

Leonid Positselski, Independent University of Moscow, Russia

Sommaire

  • Preliminaries
  • Koszul algebras and modules
  • Operations on graded algebras and modules
  • Poincaré-Birkhoff-Witt bases
  • Nonhomogeneous quadratic algebras
  • Families of quadratic algebras and Hilbert series
  • Hilbert series of Koszul algebras and one-dependent processes
  • A. DG-algebras and Massey products
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Caractéristiques techniques

  PAPIER
Éditeur(s) American Mathematical Society (AMS)
Auteur(s) Alexander Polishchuk, Leonid Positselski
Collection University Lecture Series
Parution 28/02/2006
Nb. de pages 176
Format 17,5 x 25,5
Couverture Broché
Poids 330g
Intérieur Noir et Blanc
EAN13 9780821838341
ISBN13 978-0-8218-3834-1

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