We consider a finite group acting on a vector space and the corresponding skew group algebra generated by the group and the symmetric algebra of the space. This skew group algebra illuminates the resulting orbifold and serves as a replacement for the ring of invariant polynomials, especially in the eyes of cohomology. One analyzes the Hochschild cohomology of the skew group algebra using isomor...

The extended Cuntz–Pimsner algebra E(H), introduced by Pimsner, is constructed from a Hilbert B, B–bimodule H over a C∗–algebra B. In this paper we investigate the Haagerup invariant Λ(·) for these algebras, the main result being that Λ(E(H)) = Λ(B) when H is full over B. In particular, E(H) has the completely bounded approximation property if and only if the same is true for B.

We exhibit a Poisson module restoring a twisted Poincaré duality between Poisson homology and cohomology for the polynomial algebra R = C[X1, . . . , Xn] endowed with Poisson bracket arising from a uniparametrised quantum affine space. This Poisson module is obtained as the semiclassical limit of the dualising bimodule for Hochschild homology of the corresponding quantum affine space. As a coro...

Introduction 1 1. Topological AR-quivers 2 2. Theorem of Brady-Watt and Bessis 3 3. Exceptional sequences 4 3.1. Basic definitions 5 3.2. Braid action on exceptional sequences 6 3.3. Example: Auslander-Reiten translation 7 4. Theorems about exceptional sequences 8 5. Appendix 10 5.1. Example: A2 10 5.2. More general almost split sequences 11 5.3. Bimodule of injectives 11 5.4. Untwisting in sep...

The minimal projective bimodule resolutions of the exterior algebras are explicitly constructed. They are applied to calculate the Hochschild (co)homology of the exterior algebras. Thus the cyclic homology of the exterior algebras can be calculated in case the underlying field is of characteristic zero. Moreover, the Hochschild cohomology rings of the exterior algebras are determined by generat...

In this paper we study codes where the alphabet is a finite Frobenius bimodule over a finite ring. We discuss the extension property for various weight functions. Employing an entirely character-theoretic approach and a duality theory for partitions on Frobenius bimodules we derive alternative proofs for the facts that the Hamming weight and the homogeneous weight satisfy the extension property...

A double Poisson bracket, in the sense of M. Van den Bergh, is an operation on associative algebra which induces a bracket each representation space Rep(A,n) explicit way. In this note, we study impact changing Leibniz rules underlying bracket. This change amounts to make suitable choice A-bimodule structure A⊗A. most important cases, describe how fixes analogue Jacobi identity, and obtain indu...

For a knot K and its Floer complex \(CFK^-(K)\), we introduce an algorithm to compute the bordered bimodule of complement meridian. The grading module computes \(spin^c\)-summands \({\widehat{HFK}}(S^3_{-n}(K), \mu _K)\), which can also be extended arbitrary framing n.

Inspired by a recent work of Buchweitz and Flenner, we show that, for a semidualizing bimodule $C$, $C$--perfect complexes have the ability to detect when a ring is strongly regular.It is shown that there exists a class of modules which admit minimal resolutions of $C$--projective modules.