On the semisimplicity of the outer derivations of monomial algebras
Rings and Algebras
2010-04-19 v1
Abstract
We show that the Hochschild cohomology of a monomial algebra over a field of characteristic zero vanishes from degree two if the first Hochschild cohomology is semisimple as a Lie algebra. We also prove that first Hochschild cohomology of a radical square zero algebra is reductive as a Lie algebra. In the case of the multiple loops quiver, we obtain the Lie algebra of square matrices of size equal to the number of loops.
Keywords
Cite
@article{arxiv.1004.2820,
title = {On the semisimplicity of the outer derivations of monomial algebras},
author = {Selene Sanchez-Flores},
journal= {arXiv preprint arXiv:1004.2820},
year = {2010}
}