Let A be a C∗-algebra, and let X be a Banach A-bimodule. B. E. Johnson showed that local derivations from A into X are derivations. We extend this concept of locality to the higher cohomology of a C ∗-algebra and show that, for every n ∈ N, bounded local n-cocycles from A into X are n-cocycles. The study of the local properties of Hochschild cohomology of a Banach algebra was initiated by intro...

We show that there is an action of the symmetric group on Hochschild cochain complex a twisted algebra with coefficients in bimodule. This allows us to define cohomology algebras, similarly th construction due Staic. give explicit embeddings and connecting homomorphisms between spaces algebras.

Let U be a (B, A)-bimodule, A and B rings, formal triangular matrix ring. In this paper, we characterize the structure of relative Ding projective modules over T under some conditions. Furthermore, using left global dimensions B, estimate dimension T-module.

We construct the crossed product of a C(X)-algebra by an endomorphism, in such a way that it becomes induced by a Hilbert C(X)-bimodule. Furthermore we introduce the notion of C(X)-category, and discuss relationships with crossed products and duality for compact groups.

We construct a minimal projective bimodule resolution for every finite dimensional quantum complete intersection of codimension two. Then we use this resolution to compute both the Hochschild cohomology and homology for such an algebra. In particular, we show that the cohomology vanishes in high degrees, while the homology is always nonzero.

Given a cluster-tilted algebra B we study its first Hochschild cohomology group HH(B) with coefficients in the B-B-bimodule B. We find several consequences when B is representation-finite, and also in the case where B is cluster-tilted of type Ã. 2000 Mathematics Subject Classification : 16E40

For each finite semisimple tensor category, we associate a quantum group (face algebra) whose comodule category is equivalent to the original one, in a simple natural manner. To do this, we also give a generalization of the Tannaka-Krein duality, which assigns a face algebra for each tensor category equipped with an embedding into a certain kind of bimodule category.

The first author proved in a previous paper that the n-fold bar construction for commutative algebras can be generalized to En-algebras, and that one can calculate Enhomology with trivial coefficients via this iterated bar construction. We extend this result to En-homology and En-cohomology of a commutative algebra A with coefficients in a symmetric A-bimodule.

Let Λ and Γ be artin algebras and ΛUΓ a faithfully balanced selforthogonal bimodule. We show that the U -dominant dimensions of ΛU and UΓ are identical. As applications to the results obtained, we give some characterizations of double dual functors (with respect to ΛUΓ) preserving monomorphisms and being left exact respectively.

Classical Weyl reciprocity relates the representation theories of the general linear group GLnðkÞ and the symmetric group Sr by means of the ðGLnðkÞ;SrÞ-bimodule T :1⁄4 V , where V 1⁄4 k. For example, when k 1⁄4 C, the poset 0þðn; rÞ of partitions of r with at most n non-zero parts indexes the irreducible polynomial GLnðCÞ-modules Lð Þ, which are homogeneous of degree r, and a subset of the com...