Skew group algebras of Jacobian algebras

Skew group algebras of piecewise hereditary algebras are piecewise hereditary

The aim of this paper is twofold. First, we show that the main results of HappelRickard-Schofield (1988) and Happel-Reiten-Smalø (1996) on piecewise hereditary algebras are coherent with the notion of group action on an algebra. Then, we take advantage of this compatibility and show that if G is a finite group acting on a piecewise hereditary algebra A over an algebraically closed field whose c...

Gerstenhaber Brackets for Skew Group Algebras

Hochschild cohomology governs deformations of algebras, and its graded Lie structure plays a vital role. We study this structure for the Hochschild cohomology of the skew group algebra formed by a finite group acting on an algebra by automorphisms. We examine the Gerstenhaber bracket with a view toward deformations and developing bracket formulas. We then focus on the linear group actions and p...

The Jacobian algebras

Let Pn := K[x1, . . . , xn] be a polynomial algebra over a field K of characteristic zero. The Jacobian algebra An is the subalgebra of EndK(Pn) generated by the Weyl algebra An := D(Pn) = K〈x1, . . . , xn, ∂1, . . . , ∂n〉 and the elements (∂1x1) −1, . . . , (∂nxn) −1 ∈ EndK(Pn). The algebra An appears naturally in study of the group of automorphisms of Pn. The algebra An is large since it cont...

amenability of banach algebras

chapters 1 and 2 establish the basic theory of amenability of topological groups and amenability of banach algebras. also we prove that. if g is a topological group, then r (wluc (g)) (resp. r (luc (g))) if and only if there exists a mean m on wluc (g) (resp. luc (g)) such that for every wluc (g) (resp. every luc (g)) and every element d of a dense subset d od g, m (r)m (f) holds. chapter 3 inv...

Free skew Boolean algebras