Algebras whose Tits form accepts a maximal omnipresent root
Representation Theory
2011-07-19 v1 Rings and Algebras
Abstract
Let k be an algebraically closed field and A be a finite-dimensional associative basic k-algebra of the form A=kQ/I where Q is a quiver without oriented cycles or double arrows and I is an admissible ideal of kQ. We consider roots of the Tits form q_A, in particular in case q_A is weakly non-negative. We prove that for any maximal omnipresent root v of q_A, there exists an indecomposable A-module X such that v is the dimension vector of X. Moreover, if A is strongly simply connected, the existence of a maximal omnipresent root of q_A implies that A is tame of tilted type.
Cite
@article{arxiv.1107.3299,
title = {Algebras whose Tits form accepts a maximal omnipresent root},
author = {José A. de la Peña and Andrzej Skowroński},
journal= {arXiv preprint arXiv:1107.3299},
year = {2011}
}