Cell Complexes, Poset Topology and the Representation Theory of Algebras Arising in Algebraic Combinatorics and Discrete Geometry

Franco Saliola, Benjamin Steinberg, Stuart Margolis

ISBN 10: 1470450429 / ISBN 13: 9781470450427

Published by American Mathematical Society, US, 2022

About this Item

Seller Inventory # LU-9781470450427

Bibliographic Details

• Title: Cell Complexes, Poset Topology and the Representation Theory of Algebras Arising in Algebraic Combinatorics and Discrete Geometry
• Publisher: American Mathematical Society, US
• Publication Date: 2022
• Language: English
• ISBN 10: 1470450429
• ISBN 13: 9781470450427
• Binding: Paperback
• Condition: New
• Weight: 277 grams

About this title

Synopsis

"The purpose of the present monograph is to further develop and deepen the connection between left regular bands and poset topology. This allows us to compute finite projective resolutions of all simple modules of unital left regular band algebras over fields and much more. In the process, we are led to define the class of CW left regular bands as the class of left regular bands whose associated posets are the face posets of regular CW complexes. Most of the examples that have arisen in the literature belong to this class. A new and important class of examples is a left regular band structure on the face poset of a CAT(0) cube complex. Also, the recently introduced notion of a COM (complex of oriented matroids or conditional oriented matroid) fits nicely into our setting and includes CAT(0) cube complexes and certain more general CAT(0) zonotopal complexes. A fairly complete picture of the representation theory for CW left regular bands is obtained"--