English

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)