Let $mathcal{A}$ be a Banach algebra and $mathcal{M}$ be a Banach $mathcal{A}$-bimodule. We say that a linear mapping $delta:mathcal{A} rightarrow mathcal{M}$ is a generalized $sigma$-derivation whenever there exists a $sigma$-derivation $d:mathcal{A} rightarrow mathcal{M}$ such that $delta(ab) = delta(a)sigma(b) + sigma(a)d(b)$, for all $a,b in mathcal{A}$. Giving some facts concerning general...

Let A be a ring and MA the category of right A-modules. It is well known in module theory that any A-bimodule B is an A-ring if and only if the functor − ⊗A B : MA → MA is a monad (or triple). Similarly, an A-bimodule C is an A-coring provided the functor − ⊗A C : MA → MA is a comonad (or cotriple). The related categories of modules (or algebras) of −⊗A B and comodules (or coalgebras) of − ⊗A C...

Abstract. Let G be a locally compact group, L(G) be the usual Lspace for 1 ≤ p ≤ ∞ and A(G) be the Fourier algebra ofG. Our goal is to study, in a new abstract context, the completely bounded multipliers of A(G), which we denote McbA(G). We show that McbA(G) can be characterised as the “invariant part” of the space of (completely) bounded normal L∞(G)-bimodule maps on B(L(G)), the space of boun...

Let G be an irreducible imprimitive subgroup of GLn(F), where F is a field. Any system imprimitivity for can refined to nonrefinable imprimitivity, and we consider the question when such refinement unique. Examples show that have many systems even number components not uniquely determined. We case wreath product primitive H≤GLd(F) transitive K≤Sk, n=dk. has unique except in following special ca...

Abstract. Quantum symmetric algebras (or noncommutative polynomial rings) arise in many places in mathematics. In this article we find the multiplicative structure of their Hochschild cohomology when the coefficients are in an arbitrary bimodule algebra. When this bimodule algebra is a finite group extension (under a diagonal action) of a quantum symmetric algebra, we give explicitly the graded...

A Poisson geometry arising from maximal commutative subalgebras is studied. A spectral sequence convergent to Hochschild homology with coefficients in a bimodule is presented. It depends on the choice of a maximal commutative subalgebra inducing appropriate filtrations. Its E p,q -groups are computed in terms of canonical homology with values in a Poisson module defined by a given bimodule and ...

; a ∈ A,m ∈ M, b ∈ B} equipped with the usual 2× 2 matrix-like addition and matrix-like multiplication is an algebra. An algebra T is called a triangular algebra if there exist algebras A and B and nonzero A−B-bimodule M such that T is (algebraically) isomorphic to Tri(A,M,B) under matrixlike addition and matrix-like multiplication; cf. [1]. For example, the algebra Tn of n × n upper triangular...