Topological invariants of piecewise hereditary algebras
Representation Theory
2011-01-20 v4
Abstract
We investigate the Galois coverings of piecewise algebras and more particularly their behaviour under derived equivalences. Under a technical assumption which is satisfied if the algebra is derived equivalent to a hereditary algebra, we prove that there exists a universal Galois covering whose group of automorphisms is free and depends only on the derived category of the algebra. As a corollary, we prove that the algebra is simply connected if and only if its first Hochschild cohomology vanishes.
Keywords
Cite
@article{arxiv.math/0702457,
title = {Topological invariants of piecewise hereditary algebras},
author = {Patrick Le Meur},
journal= {arXiv preprint arXiv:math/0702457},
year = {2011}
}
Comments
The hypotheses of the main theorem were modified: The next now deals mainly with piecewise hereditary algebras which are derived equivalent to a hereditary algebra (instead of all piecewise hereditary algebras in the previous version)