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Overview"Let ζ be a complex ℓ th root of unity for an odd integer ℓ>1 . For any complex simple Lie algebra g , let u ζ =u ζ (g) be the associated ""small"" quantum enveloping algebra. This algebra is a finite dimensional Hopf algebra which can be realised as a subalgebra of the Lusztig (divided power) quantum enveloping algebra U ζ and as a quotient algebra of the De Concini-Kac quantum enveloping algebra U ζ . It plays an important role in the representation theories of both U ζ and U ζ in a way analogous to that played by the restricted enveloping algebra u of a reductive group G in positive characteristic p with respect to its distribution and enveloping algebras. In general, little is known about the representation theory of quantum groups (resp., algebraic groups) when l (resp., p ) is smaller than the Coxeter number h of the underlying root system. For example, Lusztig's conjecture concerning the characters of the rational irreducible G -modules stipulates that p≥h . The main result in this paper provides a surprisingly uniform answer for the cohomology algebra H ∙ (u ζ ,C) of the small quantum group." Full Product DetailsAuthor: Christopher P. Bendel , Daniel K. Nakano , Brian J. Parshall , Cornelius PillenPublisher: American Mathematical Society Imprint: American Mathematical Society Weight: 0.172kg ISBN: 9780821891759ISBN 10: 0821891758 Pages: 93 Publication Date: 30 April 2014 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Temporarily unavailable  The supplier advises that this item is temporarily unavailable. It will be ordered for you and placed on backorder. Once it does come back in stock, we will ship it out to you. Table of ContentsPreliminaries and statement of results Quantum groups, actions, and cohomology Computation of Φ 0 and N(Φ 0 ) Combinatorics and the Steinberg module The cohomology algebra H ∙ (u ζ (g),C) Finite generation Comparison with positive characteristic Support varieties over u ζ for the modules ∇ ζ (λ) and Δ ζ (λ) Appendix A BibliographyReviewsAuthor InformationChristopher P. Bendel, University of Wisconsin-Stout, Menomonie, Wisconsin. Daniel K. Nakano, University of Georgia, Athens. Georgia, Brian J. Parshall, University of Virginia, Charlottesville, Virginia. Cornelius Pillen, University of South Alabama, Mobile, Alabama. Tab Content 6Author Website:Countries AvailableAll regions |
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