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Abstract: We prove finite generation of the cohomology ring of any finite dimensionalpointed Hopf algebra, having abelian group of grouplike elements, under somemild restrictions on the group order. The proof uses the recent classificationby Andruskiewitsch and Schneider of such Hopf algebras. Examples include all ofLusztig-s small quantum groups, whose cohomology was first computed explicitlyby Ginzburg and Kumar, as well as many new pointed Hopf algebras. We also showthat in general the cohomology ring of a Hopf algebra in a braided category isbraided commutative. As a consequence we obtain some further information aboutthe structure of the cohomology ring of a finite dimensional pointed Hopfalgebra and its related Nichols algebra.



Autor: M. Mastnak, J. Pevtsova, P. Schauenburg, S. Witherspoon

Fuente: https://arxiv.org/







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