Cohomology for quantum groups via the geometry of the nullcone / Christopher P. Bendel, Daniel K. Nakano, Brian J. Parshall, Cornelius Pillen.

Author/creator Bendel, Christopher P., 1969-
Format Electronic
Publication InfoProvidence, Rhode Island : American Mathematical Society, 2014.
Descriptionix, 93 pages ; 26 cm.
Supplemental ContentFull text available from Ebook Central - Academic Complete
Supplemental ContentFull text available from Memoirs of the American Mathematical Society
Subjects
Cohomology operations.
Algebraic topology.

Other author/creatorNakano, Daniel K. (Daniel Ken), 1964-
Other author/creatorParshall, Brian, 1945-
Other author/creatorPillen, Cornelius, 1959-
Other author/creatorAmerican Mathematical Society.
SeriesMemoirs of the American Mathematical Society, 0065-9266 ; volume 229, number 1077
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 Euler characteristic -- Induction functors -- Computation of and N -- Subroot systems defined by weights -- The case of the classical 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. 650 0 $a Cohomology operations.
Bibliography noteIncludes bibliographical references (pages 89-93).
Access restrictionAvailable only to authorized users.
Technical detailsMode of access: World Wide Web
LanguageText in English.
Genre/formElectronic books.
LCCN 2013051269
ISBN9780821891759 (pbk. : acid-free paper)
ISBN0821891758 (pbk. : acid-free paper)