The numbers of support-tilting modules for a Dynkin algebra
Representation Theory
2015-09-28 v3 Combinatorics
Abstract
The Dynkin algebras are the hereditary artin algebras of finite representation type. The paper exhibits the number of support-tilting modules for any Dynkin algebra. Since the support-tilting modules for a Dynkin algebra correspond bijectively to the non-crossing partitions of the same type, the calculations presented here may also be considered as a categorification of results concerning non-crossing partitions.
Keywords
Cite
@article{arxiv.1403.5827,
title = {The numbers of support-tilting modules for a Dynkin algebra},
author = {Mustafa A. A. Obaid and S. Khalid Nauman and Wafaa M. Fakieh and Claus Michael Ringel},
journal= {arXiv preprint arXiv:1403.5827},
year = {2015}
}
Comments
The presentation has been improved, the proof of Corollary 16 has been corrected. The previous versions included an appendix with a proof of the Ingalls-Thomas bijections for general hereditary artin algebras; it has been deleted and will be published separately