Hopf cohomology vanishing via approximation by Hochschild cohomology
Akira Masuoka (2003)
Banach Center Publications
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Akira Masuoka (2003)
Banach Center Publications
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Baker, Andrew (2000)
Homology, Homotopy and Applications
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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.
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.
Yemon Choi (2010)
Banach Center Publications
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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].
Jaume Aguadé (1981)
Mathematische Zeitschrift
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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.
Wilhelm Singhof (1978)
Mathematische Zeitschrift
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Caenepeel, S., Dăscălescu, S., Militaru, G., Panaite, F. (1997)
Bulletin of the Belgian Mathematical Society - Simon Stevin
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V. Nistor (1990)
Inventiones mathematicae
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Piotr Malicki, Andrzej Skowroński (2014)
Colloquium Mathematicae
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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.
John W. Rutter (1976)
Colloquium Mathematicae
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Volker Puppe (1979/80)
Manuscripta mathematica
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Elhamdadi, Mohamed, Gouda, Yasien Gh. (2003)
International Journal of Mathematics and Mathematical Sciences
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Pearson, Kelly Jeanne (2001)
Southwest Journal of Pure and Applied Mathematics [electronic only]
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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.
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.
Rolf Farnsteiner (1991)
Mathematische Zeitschrift
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Jean-Louis Loday (1995)
Mathematica Scandinavica
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