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

Resource Information

The instance Cohomology for quantum groups via the geometry of the nullcone, Christopher P. Bendel, Daniel K. Nakano, Brian J. Parshall, Cornelius Pillen, (electronic resource) represents a material embodiment of a distinct intellectual or artistic creation found in Bowdoin College Library. This resource is a combination of several types including: Instance, Electronic.

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Label

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

Medium

electronic resource

Statement of responsibility

Christopher P. Bendel, Daniel K. Nakano, Brian J. Parshall, Cornelius Pillen

Instantiates

• Cohomology for quantum groups via the geometry of the nullcone

Publication

• Providence, Rhode Island, American Mathematical Society, 2014

Bibliography note

Includes bibliographical references (pages 89-93)

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

Control code

ssj0001108985

Dimensions

unknown

Extent

1 online resource (ix, 93 pages)

Form of item

online

Governing access note

Access restricted to subscribing institutions

Isbn

9780821891759

Isbn Type

(pbk. : acid-free paper)

Lccn

2013051269

Record ID

.b64265924

Specific material designation

remote

System control number

(WaSeSS)ssj0001108985