Topological invariants of piecewise hereditary algebras

Details Topological invariants of piecewise hereditary algebras Topological invariants of piecewise hereditary algebras

2007-02-15

arxiv.org/abs/math/0702457v4

Transactions of the American Mathematical Society 363, 4 (2011) 2143--2170

Mathematics

Representation Theory

The hypotheses of the main theorem were modified: The next now deals mainly with piecewise hereditary algebras which are deriv

Scientific paper

10.1090/S0002-9947-2010-05185-2

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.

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