Tate and Tate�Hochschild cohomology for finite dimensional Hopf algebras
- Autores: Van C. Nguyen
- Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 217, Nº 10, 2013, págs. 1967-1979
- Idioma: inglés
- DOI: 10.1016/j.jpaa.2013.01.008
- Enlaces
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Resumen
Let A be any finite dimensional Hopf algebra over a field k. We specify the Tate and Tate�Hochschild cohomology for A and introduce cup products that make them become graded rings. We establish the relationship between these rings. In particular, the Tate� Hochschild cohomology of A is isomorphic (as algebras) to its Tate cohomology with coefficients in an adjoint module. Consequently, the Tate cohomology ring of A is a direct summand of its Tate�Hochschild cohomology ring. As an example, we explicitly compute both the Tate and Tate�Hochschild cohomology for the Sweedler algebra H4.
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