Recent Developments in Representation Theory
About this Title
Alex Martsinkovsky, Northeastern University, Boston, MA, Gordana Todorov, Northeastern University, Boston, MA and Kiyoshi Igusa, Brandeis University, Waltham, MA, Editors
Publication: Contemporary Mathematics
Publication Year: 2016; Volume 673
ISBNs: 978-1-4704-1955-4 (print); 978-1-4704-3530-1 (online)
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.
Graduate students and research mathematicians interested in combinatorial aspects of representation theory of algebra.
Table of Contents
- V. V. Bavula – Orders in Artinian rings, Goldie’s Theorem and the largest left quotient ring of a ring
- Ellen E. Kirkman – Invariant theory of Artin-Schelter regular algebras: a survey
- Claus Michael Ringel – The Catalan combinatorics of the hereditary artin algebras
- Evgeny Smirnov – Grassmannians, flag varieties, and Gelfand–Zetlin polytopes
- Luise Unger – On the combinatorics of the set of tilting modules