We characterize the derivation d : A→ ΩDer(A) by a universal property introducing a new class of bimodules. Abridged English Version In this Note, A denotes an associative algebra over K = R or C with a unit 1l. In the Note [5], a graded differential algebra ΩDer(A) with Ω 0 Der(A) = A was introduced with the notation ΩD(A). It is one of the aims of this Note to show that, by introducing a new ...

We give a sufficient condition for a bi-invariant weight on a Frobenius bimodule to satisfy the extension property. This condition applies to bi-invariant weights on a finite Frobenius ring as a special case. The complex-valued functions on a Frobenius bimodule are viewed as a module over the semigroup ring of the multiplicative semigroup of the coefficient ring.

as (G,G)-bimodules, and where the sum is over all irreducible representations of G. Let H be a Hopf algebra. If H is finite dimensional, then H∗ is also a Hopf algebra by dualizing all operations from H. We run into issues if H is infinite-dimensional, but we can find a fix. For a finite-dimensional H-module V , an element v ∈ V , and f ∈ V ∗, define a linear functional on H by cf,v(u) = f(uv)....

Let R and S be arbitrary associative rings. Given a bimodule RWS , we denote by ∆? and Γ? the functors Hom?(−, W ) and Ext?(−, W ), where ? = R or S. We say that RWS is a finitistic weakly cotilting bimodule (briefly FWC) if for each module M cogenerated by W , finitely generated or homomorphic image of a finite direct sum of copies of W , ΓM = 0 = Ext(M, W ). We are able to describe, on a larg...

Let k be an algebraically closed field of characteristic p. We shall discuss the cohomology algebras of a block ideal B of the group algebra kG of a finite group G and a block ideal C of the block ideal of kH of a subgroup H of G which are in Brauer correspondence and have a common defect group, continuing [4]. We shall define a (B,C)-bimodule L. The k-dual L∗ induces the transfer map between t...

For a given endomorphism on a unitary k-algebra, A, with k in the center of A, there are definitions of twisted cyclic and Hochschild homology. This paper will show that the method used to define them can be used to define twisted de Rham homology. The main result is that twisted de Rham homology can be thought of as the kernel of the Connes map from twisted cyclic homology to twisted Hochschil...

Frames in Hilbert bimodules are a special case of frames in Hilbert C*-modules. The paper considers A-frames and B-frames and their relationship in a Hilbert A-B-imprimitivity bimodule. Also, it is given that every frame in Hilbert spaces or Hilbert C*-modules is a semi-tight frame. A relation between A-frames and K(H_B)-frames is obtained in a Hilbert A-B-imprimitivity bimodule. Moreover, the ...

A continuous one-parameter group of unitary isometries of a right-Hilbert C*bimodule induces a quasi-free dynamics on the Cuntz-Pimsner C*-algebra of the bimodule and on its Toeplitz extension. The restriction of such a dynamics to the algebra of coefficients of the bimodule is trivial, and the corresponding KMS states of the Toeplitz-Cuntz-Pimsner and Cuntz-Pimsner C*-algebras are characterize...