PIECEWISE HEREDITARY SKEW GROUP ALGEBRAS
LIPING LI
Abstract. Let # be a finite dimensional algebra and G be a finite group whose elements act on # as algebra automorphisms. Under the assumption that # has a complete set E of primitive orthogonal idempotents, closed under the action of a Sylow p-subgroup S # G, we show that the skew group algebra #G and # have the same finitistic dimension and the same strong global di- mension if the action of S on E is free. Using a homological characterization of piecewise hereditary algebras proved by Happel and Zacharia, we deduce that #G is piecewise hereditary if and only if S acts freely on E and # is piecewise hereditary as well.