Algebra extensions A ⊆ B where A is a left B-module such that the Baction extends the multiplication in A are ubiquitous. We encounter examples of such extensions in the study of group actions, group gradings or more general Hopf actions as well as in the study of the bimodule structure of an algebra. In this paper we are extending R.Wisbauer’s method of constructing the central closure of a se...

This paper deals with the boundary value problem involving the differential equation ell y:=-y''+qy=lambda y, subject to the eigenparameter dependent boundary conditions along with the following discontinuity conditions y(d+0)=a y(d-0), y'(d+0)=ay'(d-0)+b y(d-0). In this problem q(x), d, a , b are real, qin L^2(0,pi), din(0,pi) and lambda is a parameter independent of x. By defining a new...

Let A be a unital R-algebra and M be a unital A-bimodule. It is shown that every Jordan derivation of the trivial extension of A by M, under some conditions, is the sum of a derivation and an antiderivation.

Let A be a (G, χ)-Hopf algebra with bijection antipode and let M be a G-graded A-bimodule. We prove that there exists an isomorphism HH∗gr(A,M) ∼= Ext ∗ A-gr(K, (M)), where K is viewed as the trivial graded A-module via the counit of A, M is the adjoint A-module associated to the graded A-bimodule M and HHgr denotes the G-graded Hochschild cohomology. As an application, we deduce that the cohom...

Based on the usual Fedosov construction of star products for a symplectic manifold M we give a simple geometric construction of a bimodule deformation for the sections of a vector bundle over M starting with a symplectic connection on M and a connection for E. In the case of a line bundle this gives a Morita equivalence bimodule where the relation between the characteristic classes of the Morit...

Finite quantum groupoids can be described in many equivalent ways [8, 11, 16]: In terms of the weak Hopf C -algebras of Böhm, Nill, and Szlachányi [2] or the finite-dimensional Hopf-von Neumann bimodules of Vallin [14], and in terms of finite-dimensional multiplicative partial isometries [4] or the finite-dimensional pseudo-multiplicative unitaries of Vallin [15]. In this note, we show that in ...

Given, on the Hilbert space H0, the self-adjoint operator B and the skew-adjoint operators C1 and C2, we consider, on the Hilbert space H ≃ D(B)⊕H0, the skew-adjoint operator

A CP -semigroup (or quantum dynamical semigroup) is a semigroup φ = {φt : t ≥ 0} of normal completely positive linear maps on B(H), H being a separable Hilbert space, which satisfies φt(1) = 1 for all t and is continuous in the natural sense. Let D be the natural domain of the generator L of φ, φt = exp tL. Since the maps φt need not be multiplicative D is typically an operator space, but not a...