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Item Details
| Title:
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COHOMOLOGY FOR QUANTUM GROUPS VIA THE GEOMETRY OF THE NULLCONE
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| By: |
Christopher P. Bendel, Daniel K. Nakano, Brian J. Parshall |
| Format: |
Microfilm |
| List price:
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£67.00 |
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We believe that this item is permanently unavailable, and so we cannot source
it.
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| ISBN 10: |
0821891758 |
| ISBN 13: |
9780821891759 |
| Publisher: |
AMERICAN MATHEMATICAL SOCIETY |
| Pub. date: |
30 April, 2014 |
| Series: |
Memoirs of the American Mathematical Society 229/1077 |
| Pages: |
93 |
| Synopsis: |
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. |
| Publication: |
US |
| Imprint: |
American Mathematical Society |
| Returns: |
Returnable |
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