Cohomology for Quantum Groups Via the Geometry of the Nullcone - Brossura

Bendel, Christopher P.; Nakano, Daniel K.; Parshall, Brian J.; Pillen, Cornelius

Brossura

ISBN 10: 0821891758 ISBN 13: 9780821891759

Casa editrice: Amer Mathematical Society, 2014

Riassunto

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.

Dettagli dell'edizione

• Editore: Amer Mathematical Society
• Data di pubblicazione: 2014
• Lingua: Inglese
• ISBN 10: 0821891758
• ISBN 13: 9780821891759
• Rilegatura: Copertina flessibile
• Numero di pagine: 93
• Contatto del produttore: non disponibile
• Persona responsabile: non disponibile