Cohomology of finite dimensional pointed Hopf algebras

Autor:	Mastnak, M., Pevtsova, J., Schauenburg, P., Witherspoon, S.
Rok vydání:	2009
Předmět:	Mathematics - Rings and Algebras Mathematics - K-Theory and Homology Mathematics - Representation Theory 16E40 16W30
Druh dokumentu:	Working Paper
DOI:	10.1112/plms/pdp030
Popis:	We prove finite generation of the cohomology ring of any finite dimensional pointed Hopf algebra, having abelian group of grouplike 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. Comment: 36 pages, references added
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/0902.0801 Zobrazit plný text záznamu View this record from Arxiv