Cohomology for quantum groups via the geometry of the nullcone
Preliminaries and Statement of resultsSome 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) -- Adjoi...
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| Weitere Verfasser: | , , , |
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| Format: | UnknownFormat |
| Sprache: | eng |
| Veröffentlicht: |
Providence, RI
American Math. Soc.
c2013
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| Schriftenreihe: | Memoirs of the American Mathematical Society
1077 = Vol. 229,[4] |
| Schlagworte: | |
| Online Zugang: | Inhaltsverzeichnis Inhaltstext |
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Tag hinzufügen | Zusammenfassung: | Preliminaries and Statement of resultsSome 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. |
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| Beschreibung: | "Volume 229, number 1077 (fourth of 5 numbers), May 2014". - Includes bibliographical references and index |
| Beschreibung: | IX, 93 S. |
| ISBN: | 9780821891759 978-0-8218-9175-9 |