Cohomology for Quantum Groups via the Geometry of the Nullcone (inbunden)
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Format
Häftad (Paperback / softback)
Språk
Engelska
Serie
Memoirs of the American Mathematical Society
Utgivningsdatum
2014-09-22
Förlag
American Mathematical Society
ISBN
9780821891759

Cohomology for Quantum Groups via the Geometry of the Nullcone

av Christopher P Bendel, Daniel K Nakano, Brian J Parshall, Cornelius Pillen
Häftad,  Engelska, 2014-09-22
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Let ? be a complex ? th root of unity for an odd integer ?>1 . For any complex simple Lie algebra g , let u ? =u ? (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 ? and as a quotient algebra of the De Concini-Kac quantum enveloping algebra U ? . It plays an important role in the representation theories of both U ? and U ? 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 ? ,C) of the small quantum group.
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Övrig information

Christopher 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.

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