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Recent developments in representation theory / [edited by] Alex Martsinkovsky, Gordana Todorov and Kiyoshi Igusa.

By: Contributor(s): Material type: TextTextSeries: Contemporary mathematics ; 673.Publication details: Providence : American Mathematical Society, ©2016.Description: v, 249 pages : illustrations ; 25 cmISBN:
  • 9781470419554 (alk. paper)
Subject(s): DDC classification:
  • 510 23 Am512c
Contents:
Orders in Artinian rings, Goldie's Theorem and the largest left quotient ring of a ring / V. V. Bavula -- Invariant theory of Artin-Schelter regular algebras: a survey / Ellen E. Kirkman -- The Catalan combinatorics of the hereditary artin algebras / Claus Michael Ringel -- Grassmannians, flag varieties, and Gelfand-Zetlin polytopes / Evgeny Smirnov -- On the combinatorics of the set of tilting modules / Luise Unger --
Summary: This volume contains selected expository lectures delivered at the Maurice Auslander Distinguished Lectures and International Conference, held May 1-6, 2014, at the Woods Hole Oceanographic Institute, Woods Hole, MA. Several significant developments of the last decade in representation theory of finite-dimensional algebras are related to combinatorics. Three of the five lectures in this volume deal, respectively, with the Catalan combinatorics, the combinatorics of Gelfand-Zetlin polytopes, and the combinatorics of tilting modules. The remaining papers present history and recent advances in the study of left orders in left Artinian rings and a survey on invariant theory of Artin-Schelter regular algebras.
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Includes bibliographical references.

Orders in Artinian rings, Goldie's Theorem and the largest left quotient ring of a ring / V. V. Bavula --
Invariant theory of Artin-Schelter regular algebras: a survey / Ellen E. Kirkman --
The Catalan combinatorics of the hereditary artin algebras / Claus Michael Ringel --
Grassmannians, flag varieties, and Gelfand-Zetlin polytopes / Evgeny Smirnov --
On the combinatorics of the set of tilting modules / Luise Unger --

This volume contains selected expository lectures delivered at the Maurice Auslander Distinguished Lectures and International Conference, held May 1-6, 2014, at the Woods Hole Oceanographic Institute, Woods Hole, MA. Several significant developments of the last decade in representation theory of finite-dimensional algebras are related to combinatorics. Three of the five lectures in this volume deal, respectively, with the Catalan combinatorics, the combinatorics of Gelfand-Zetlin polytopes, and the combinatorics of tilting modules. The remaining papers present history and recent advances in the study of left orders in left Artinian rings and a survey on invariant theory of Artin-Schelter regular algebras.

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