Cohomology of finite-dimensional pointed Hopf algebras

Mastnak, M.; Pevtsova, J.; Schauenburg, Peter; Witherspoon, S.

Cohomology of finite-dimensional pointed Hopf algebras

Dateien

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Datum

2009

Autor:innen

Mastnak, M.

Pevtsova, J.

Schauenburg, Peter

Witherspoon, S.

Publikationstyp

Zeitschriftenartikel

Erschienen in

Proceedings of the London Mathematical Society ; 100 (2009), 2. - S. 377-404. - ISSN 0024-6115

Zusammenfassung

We prove finite generation of the cohomology ring of any finite-dimensional pointed Hopf algebra, having abelian group of group-like elements, under some mild restrictions on the group order. The proof uses the recent classification by Andruskiewitsch and Schneider of such Hopf algebras. Examples include all of Lusztig's small quantum groups, whose cohomology was first computed explicitly by Ginzburg and Kumar, as well as many new pointed Hopf algebras. We also show that in general the cohomology ring of a Hopf algebra in a braided category is braided commutative. As a consequence we obtain some further information about the structure of the cohomology ring of a finite-dimensional pointed Hopf algebra and its related Nichols algebra.

Fachgebiet (DDC)

510 Mathematik

Zitieren

ISO 690

MASTNAK, M., J. PEVTSOVA, Peter SCHAUENBURG, S. WITHERSPOON, 2009. Cohomology of finite-dimensional pointed Hopf algebras. In: Proceedings of the London Mathematical Society. 100(2), pp. 377-404. ISSN 0024-6115. Available under: doi: 10.1112/plms/pdp030

BibTex

@article{Mastnak2009Cohom-12762,
  year={2009},
  doi={10.1112/plms/pdp030},
  title={Cohomology of finite-dimensional pointed Hopf algebras},
  number={2},
  volume={100},
  issn={0024-6115},
  journal={Proceedings of the London Mathematical Society},
  pages={377--404},
  author={Mastnak, M. and Pevtsova, J. and Schauenburg, Peter and Witherspoon, S.}
}

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