Skew group algebras of piecewise hereditary algebras are piecewise hereditary

Derived equivalence classification of generalized multifold extensions of piecewise hereditary algebras of tree type

We give a derived equivalence classification of algebras of the form Â/〈φ〉 for some piecewise hereditary algebra A of tree type and some automorphism φ of  such that φ(A) = A for some positive integer n.

Ideal Amenability of Banach Algebras and Some Hereditary Properties

Let A be a Banach algebra. A is called ideally amenable if for every closed ideal I of A, the first cohomology group of A with coefficients in I* is trivial. We investigate the closed ideals I for which H1 (A,I* )={0}, whenever A is weakly amenable or a biflat Banach algebra. Also we give some hereditary properties of ideal amenability.

Topological Invariants of Piecewise Hereditary Algebras

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...

Hereditary properties of amenability modulo an ideal of Banach algebras

In this paper we investigate some hereditary properties of amenability modulo an ideal of Banach algebras. We show that if $(e_alpha)_alpha$ is a bounded approximate identity modulo I of a Banach algebra A and X is a neo-unital modulo I, then $(e_alpha)_alpha$ is a bounded approximate identity for X. Moreover we show that amenability modulo an ideal of a Banach algebra A can be only considered ...

Derived and Stable Equivalence Classification of Twisted Multifold Extensions of Piecewise Hereditary Algebras of Tree Type