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Displaying similar documents to “Hopf-type Cyclic Cohomology via the Karoubi Operator”

Cyclic cohomology of (extended) Hopf algebras

M. Khalkhali, B. Rangipour (2003)

Banach Center Publications

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We review recent progress in the study of cyclic cohomology of Hopf algebras, extended Hopf algebras, invariant cyclic homology, and Hopf-cyclic homology with coefficients, starting with the pioneering work of Connes-Moscovici.

Distinguishing derived equivalence classes using the second Hochschild cohomology group

Deena Al-Kadi (2010)

Colloquium Mathematicae

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We study the second Hochschild cohomology group of the preprojective algebra of type D₄ over an algebraically closed field K of characteristic 2. We also calculate the second Hochschild cohomology group of a non-standard algebra which arises as a socle deformation of this preprojective algebra and so show that the two algebras are not derived equivalent. This answers a question raised by Holm and Skowroński.

Splitting maps and norm bounds for the cyclic cohomology of biflat Banach algebras

Yemon Choi (2010)

Banach Center Publications

Similarity:

We revisit the old result that biflat Banach algebras have the same cyclic cohomology as C, and obtain a quantitative variant (which is needed in separate, joint work of the author on the simplicial and cyclic cohomology of band semigroup algebras). Our approach does not rely on the Connes-Tsygan exact sequence, but is motivated strongly by its construction as found in [2] and [5].

Excision in entire cyclic cohomology

Ralf Meyer (2001)

Journal of the European Mathematical Society

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We prove that entire and periodic cyclic cohomology satisfy excision for extensions of bornological algebras with a bounded linear section. That is, for such an extension we obtain a six term exact sequence in cohomology.

Hochschild cohomology of generalized multicoil algebras

Piotr Malicki, Andrzej Skowroński (2014)

Colloquium Mathematicae

Similarity:

We determine the Hochschild cohomology of all finite-dimensional generalized multicoil algebras over an algebraically closed field, which are the algebras for which the Auslander-Reiten quiver admits a separating family of almost cyclic coherent components. In particular, the analytically rigid generalized multicoil algebras are described.

On complements and the factorization problem of Hopf algebras

Sebastian Burciu (2011)

Open Mathematics

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Two new results concerning complements in a semisimple Hopf algebra are proved. They extend some well-known results from group theory. The uniqueness of a Krull-Schmidt-Remak type decomposition is proved for semisimple completely reducible Hopf algebras.

Cutting description of trivial 1-cohomology

Andrzej Czarnecki (2014)

Annales Polonici Mathematici

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A characterisation of trivial 1-cohomology, in terms of some connectedness condition, is presented for a broad class of metric spaces.