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Cohomology for Quantum Groups via the Geometry of the Nullcone / Christopher P. Bendel, Daniel K. Nakano, Brian J. Parshall, Cornelius Pillen.
Math/Physics/Astronomy Library QA3 .A57 no.1077
Available
- Format:
- Book
- Author/Creator:
- Bendel, Christopher P., 1969- author.
- Nakano, Daniel K. (Daniel Ken), 1964- author.
- Parshall, Brian, 1945- author.
- Pillen, Cornelius, 1959- author.
- Series:
- Memoirs of the American Mathematical Society ; no. 1077.
- Memoirs of the American Mathematical Society, 0065-9266 ; number 1077
- Language:
- English
- Subjects (All):
- Cohomology operations.
- Algebraic topology.
- Physical Description:
- ix, 93 pages ; 26 cm.
- Place of Publication:
- Providence, Rhode Island : American Mathematical Society, 2014.
- Language Note:
- Text in English.
- Contents:
- Preliminaries and Statement of results
- Some preliminary notation
- Main results
- Quantum groups, actions, and cohomology
- Listings
- Quantum enveloping algebras
- Connections with algebraic groups
- Root vectors and PBW-basis
- Levi and parabolic subalgebras
- The subalgebra Uq(uj)
- Adjoint action
- Finite dimensionality of cohomology groups
- Spectral sequences and the Euler characteristic
- Induction functors
- Computation of and N
- Subroot systems defined by weights
- The case of the classical Lie algebras
- The case of the exceptional Lie algebras
- Standardizing
- Resolution of singularities
- Normality of orbit closures
- Combinatorics and the Steinberg Module
- Steinberg weights
- Weights of
- Multiplicity of the Steinberg module
- Proof of Proposition 4.2.1
- The weight
- Types Bn, Cn, Dn
- Type An
- Type An with l dividing n + 1
- Exceptional Lie algebras
- The Cohomology Algebra H
- Spectral sequences, I
- Spectral sequences, II
- An identification theorem
- Spectral sequences, III
- Proof of main result, Theorem 1.2.3, I
- Spectral sequences, IV
- Proof of the main result, Theorem 1.2.3, II
- Finite Generation
- A finite generation result
- Proof of part (a) of Theorem 1.2.4
- Proof of part (b) of Theorem 1.2.4
- Comparison with Positive Characteristic
- The setting
- Assumptions
- Consequences
- Special cases
- Support Varieties over for the Modules and
- Quantum support varieties
- Lower bounds on the dimensions of support varieties
- Support varieties of : general results
- Support varieties of when l is good
- A question of naturality of support varieties
- The Constrictor Method I
- The Constrictor Method II
- Support varieties of when l is bad
- E6 when 3 l
- F4 when 3 l
- E7 when 3 l
- E8 when 3 l, 5 l
- Support varieties of when l is bad.
- Notes:
- Includes bibliographical references.
- ISBN:
- 9780821891759
- 0821891758
- OCLC:
- 867024601
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