First cohomology for finite groups of Lie type: Simple modules with small dominant weights

DOI10.1090/S0002-9947-2012-05664-9zbMath1295.20059arXiv1010.1203WikidataQ115285555 ScholiaQ115285555MaRDI QIDQ4915122

University of Georgia VIGRE Algebra Group

Publication date: 16 April 2013

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1010.1203

zbMATH Keywords

algebraic groupscohomologyfinite groups of Lie typeFrobenius kernelsBorel subgroupsunipotent radicalfinite Chevalley groupsrestriction mapsfundamental dominant weightsalgebraic group schemescohomology groups of simple modules

Mathematics Subject Classification ID

Representation theory for linear algebraic groups (20G05) Cohomology of groups (20J06) Representations of finite groups of Lie type (20C33) Cohomology theory for linear algebraic groups (20G10)

Related Items (5)

On tensoring with the Steinberg representation ⋮ Extensions for finite Chevalley groups. III: Rational and generic cohomology. ⋮ Divisibility questions in commutative algebraic groups ⋮ Local-global questions for divisibility in commutative algebraic groups ⋮ Bounding the Dimensions of Rational Cohomology Groups

Uses Software

• GAP

Cites Work

• Bounding Ext for modules for algebraic groups, finite groups and quantum groups.
• First cohomology groups of Chevalley groups in cross characteristic.
• Some applications of the first cohomology group
• Cohomology of infinitesimal and discrete groups
• Some representations of exceptional Lie algebras
• Rational and generic cohomology
• Cohomology of finite groups of Lie type. I
• Complexity for modules over finite Chevalley groups and classical Lie algebras
• Some new examples in 1-cohomology
• Modular elliptic curves and Fermat's Last Theorem
• On extensions of simple modules over symmetric and algebraic groups
• Weil restriction and support varieties
• Extensions of Modules for Algebraic Groups
• Cohomology of algebraic groups, finite groups, and Lie algebras: Interactions and Connections
• Homology
• Corrigendum: ``On extensions of simple modules over symmetric and algebraic groups
• On comparing the cohomology of algebraic groups, finite Chevalley groups and Frobenius kernels
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