Cohomology of finite-dimensional pointed Hopf algebras

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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

@article{Mastnak2009Cohom-12762, title={Cohomology of finite-dimensional pointed Hopf algebras}, year={2009}, doi={10.1112/plms/pdp030}, 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.} }

<rdf:RDF xmlns:dcterms="" xmlns:dc="" xmlns:rdf="" xmlns:bibo="" xmlns:dspace="" xmlns:foaf="" xmlns:void="" xmlns:xsd="" > <rdf:Description rdf:about=""> <dc:language>eng</dc:language> <dcterms:issued>2009</dcterms:issued> <dcterms:available rdf:datatype="">2011-09-07T09:11:27Z</dcterms:available> <dcterms:abstract xml:lang="eng">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.</dcterms:abstract> <dcterms:bibliographicCitation>Publ. in: Proceedings of the London Mathematical Society ; 100 (2010), 2. - pp. 377-404</dcterms:bibliographicCitation> <dc:creator>Witherspoon, S.</dc:creator> <bibo:uri rdf:resource=""/> <dc:contributor>Witherspoon, S.</dc:contributor> <dc:contributor>Pevtsova, J.</dc:contributor> <dc:creator>Schauenburg, Peter</dc:creator> <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/> <dspace:isPartOfCollection rdf:resource=""/> <dc:rights>terms-of-use</dc:rights> <dcterms:rights rdf:resource=""/> <foaf:homepage rdf:resource="http://localhost:8080/jspui"/> <dc:creator>Pevtsova, J.</dc:creator> <dc:creator>Mastnak, M.</dc:creator> <dcterms:isPartOf rdf:resource=""/> <dc:contributor>Schauenburg, Peter</dc:contributor> <dc:contributor>Mastnak, M.</dc:contributor> <dcterms:title>Cohomology of finite-dimensional pointed Hopf algebras</dcterms:title> <dc:date rdf:datatype="">2011-09-07T09:11:27Z</dc:date> </rdf:Description> </rdf:RDF>

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