Endomorphism algebras for a class of negative Calabi-Yau categories
Representation Theory
2016-02-18 v2 Combinatorics
Abstract
We consider an orbit category of the bounded derived category of a path algebra of type A_n which can be viewed as a -(m+1)-cluster category, for m >= 1. In particular, we give a characterisation of those maximal m-rigid objects whose endomorphism algebras are connected, and then use it to explicitly study these algebras. Specifically, we give a full description of them in terms of quivers and relations, and relate them with (higher) cluster-tilted algebras of type A. As a by-product, we introduce a larger class of algebras, called 'tiling algebras'.
Keywords
Cite
@article{arxiv.1602.02318,
title = {Endomorphism algebras for a class of negative Calabi-Yau categories},
author = {Raquel Coelho Simoes and Mark James Parsons},
journal= {arXiv preprint arXiv:1602.02318},
year = {2016}
}
Comments
Second version with minor corrections and improved presentation, 20 pages, 4 figures