Let U = Tri(A,M,B) be a triangular algebra, where A, B are unital algebras over a field F and M is a faithful (A,B)-bimodule. Assume that ξ ∈ F and L : U → U is a map. It is shown that, under some mild conditions, L is linear and satisfies L([X, Y ]) = [L(X), Y ] + [X,L(Y )] for any X,Y ∈ U with [X, Y ] = XY − Y X = 0 if and only if L(X) = φ(X) + ZX + f(X) for all A, where φ is a linear derivat...

Mansfield showed how to induce representations of crossed products of C∗algebras by coactions from crossed products by quotient groups and proved an imprimitivity theorem characterising these induced representations. We give an alternative construction of his bimodule in the case of dual coactions, based on the symmetric imprimitivity theorem of the third author; this provides a more workable w...

We study pseudo-Riemannian invariant metrics on bicovariant bimodules over Hopf algebras. clarify some properties of such and prove that a bimodule its cocycle deformations are in one to correspondence.

in this paper, we introduce a notion of property (t) for a c∗-dynamical system (a, g, α) consisting of a unital c∗-algebra a,a locally compact group g, and an action α on a. as a result,we show that if a has strong property (t) and g has kazhdan’sproperty (t), then the triple (a, g, α) has property (t).

It is proved that the second cohomology group of the conformal algebras Cendn and Curn with coefficients in any bimodule is trivial. As a result, these algebras are segregated in any extension with a nilpotent kernel.

Amonge other things we give sufficient and necessary conditions for the Lau product of Banachalgebras to be biflat or biprojective.

We give two sufficient and necessary conditions for the Hochschild extension of a finite-dimensional algebra by its dual bimodule 2-cocycle to be symmetric algebra.

In this section we shall assume that all algebras are finite dimensional algebras over an algebraically closed field F. The fact that F is algebraically closed is only for convenience, to avoid the division rings that could arise in the decomposition of Ā just before (4.8) below. Let A ⊆ B be an inclusion of algebras. Then B⊗F B is an (A,A)-bimodule where A acts on the left by left multiplicati...

By a well known theorem of K. Morita, any equivalence between full module categories over rings R and S, are given by a bimodule RPS , such that RP is a finitely generated projective generator in R-Mod and S = EndR(P ). There are various papers which describe equivalences between certain subcategories of R-Mod and S-Mod in a similar way with suitable properties of RPS . Here we start from the o...