Subalgebra depths within the path algebra of an acyclic quiver
Representation Theory
2013-02-08 v1
Abstract
Constraints are given on the depth of diagonal subalgebras in generalized triangular matrix algebras. The depth of the top subalgebra B = A /rad A in a finite, connected, acyclic quiver algebra A over an algebraically closed field K is then computed. Also the depth of the primary arrow subalgebra 1K + rad A = B in A is obtained. The two types of subalgebras have depths 3 and 4 respectively, independent of the number of vertices. An upper bound on depth is obtained for the quotient of a subalgebra pair.
Keywords
Cite
@article{arxiv.1302.1730,
title = {Subalgebra depths within the path algebra of an acyclic quiver},
author = {Lars Kadison and Christopher J. Young},
journal= {arXiv preprint arXiv:1302.1730},
year = {2013}
}
Comments
14 pp. to appear in Proceedings A.G.M.P. Conf. Mulhouse, 2011, Springer