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Relative cyclic homology of square zero extensions
Jorge A. Guccione, Juan J. Guccione
Let k be a characteristic zero field, C a k-algebra and M a square zero two sided ideal of C. We obtain a new mixed complex, simpler that the canonical one, giving the Hochschild a…
Hochschild cohomology of Frobenius algebras
Jorge A. Guccione, Juan J. Guccione
Let k be a field and let A be a Frobenius algebra over k. Assume that the Nakayama automorphism of A associated to a Frobenius homomorphism of A has finite order m, and k has a m-t…
Hochschild homology of iterate skew polynomial rings
Jorge A. Guccione, Juan J. Guccione
We study the Hochschild homology of the iterated skew polynomial rings introduced by D. Jordan in ``A simple localization of the quantized Weyl algebra''. First, we obtain a comple…
Cohomology of trivial extensions of Frobenius algebras
Jorge A. Guccione, Juan J. Guccione
We obtain a decomposition for the Hochschild cochain complex of a split algebra and we study some properties of the cohomology of each term of this decomposition. Then, we consider…
Hochschild cohomology of triangular matrix algebras
Jorge A. Guccione, Juan J. Guccione
We prove the existence of two long exact sequences relating the Hochschild cohomology of a triangular matrix algebra with the Hochschild homology of its component subalgebras. We a…
Hochschild (co)homology of Hopf crossed products
Jorge A. Guccione, Juan J. Guccione
Let A a k-algebra, H a Hopf algebra, E = A#H a general crossed product and M an E-bimodule. We obtain a complex simpler than the canonical one, giving the Hochschild homology of E…