Cohomology for quantum groups via the geometry of the nullcone
By: Christopher P. Bendel, Daniel K. Nakano, Brian J. Parshall, Cornelius Pillen
Contributors: Nakano, Daniel K. (Daniel Ken), 1964-; Parshall, Brian, 1945-; Pillen, Cornelius, 1959-; American Mathematical Society
Series: Memoirs of the American Mathematical Society -- volume 229, number 1077
Publisher: American Mathematical Society
Published: 2014
Place of publication: Providence, Rhode Island
Language: eng
Number of pages: 93
ISBN-13: 9780821891759
Subjects: Cohomology operations; Algebraic topology
Notes: Includes bibliographical references (pages 89-93).

Text in English.
Table of contents: title: Preliminaries and Statement of results; title: Some preliminary notation; title: Main results; title: Quantum groups, actions, and cohomology; title: Listings; title: Quantum enveloping algebras; title: Connections with algebraic groups; title: Root vectors and PBW-basis; title: Levi and parabolic subalgebras; title: The subalgebra Uq(uj); title: Adjoint action; title: Finite dimensionality of cohomology groups; title: Spectral sequences and Euler characteristic; title: Induction functors; title: Computation of and N; title: Subroot systems defined by weights; title: The case of the classical Lie algebras; title: Standardizing; title: Resolution of singularities; title: Normality of orbit closures; title: Combinatorics and the Steinberg Module; title: Steinberg weights; title: Weights of; title: Multiplicity of the Steinberg module; title: Proof of Proposition 4.2.1; title: The weight; title: Types Bn, Cn, Dn; title: Type An; title: Type An with l dividing n + 1; title: Exceptional Lie algebras; title: The Cohomology Algebra H; title: Spectral sequences, I; title: Spectral sequences, II; title: An identification theorem; title: Spectral sequences, III; title: Proof of main result, Theorem 1.2.3, I; title: Spectral sequences, IV; title: Proof of the main result, Theorem 1.2.3, II; title: Finite Generation; title: A finite generation result; title: Proof of part (a) of Theorem 1.2.4; title: Proof of part (b) of Theorem 1.2.4; title: Comparison with Positive Characteristic; title: The setting; title: Assumptions; title: Consequences; title: Special cases; title: Support Varieties over for the Modules and; title: Quantum support varieties; title: Lower bounds on the dimensions of support varieties; title: Support varieties of : general results; title: Support varieties of when l is good; title: A question of naturality of support varieties; title: The Constrictor Method I; title: The Constrictor Method II; title: Support varieties of when l is bad; title: E6 when 3  l; title: F4 when 3  l; title: E7 when 3  l; title: E8 when 3  l, 5  l; title: Support varieties of when l is bad.  650  0 $a Cohomology operations.