Adjoint invariants of second Frobenius kernels of GL(2)

2020 ◽  
Vol 48 (11) ◽  
pp. 4969-4988
Author(s):  
František Marko
Keyword(s):  
Frobenius Kernels

scholarly journals HIGHER DEFORMATIONS OF LIE ALGEBRA REPRESENTATIONS II

2020 ◽  
pp. 1-24
Author(s):  
MATTHEW WESTAWAY
Keyword(s):  
Tensor Product ◽  
Algebraic Groups ◽  
Preceding Paper ◽  
Irreducible Representations ◽  
Product Theorem ◽  
Enveloping Algebras ◽  
Frobenius Kernel ◽  
Frobenius Kernels ◽  
Lie Algebra Representations ◽  
Semisimple Algebraic Groups

Steinberg’s tensor product theorem shows that for semisimple algebraic groups, the study of irreducible representations of higher Frobenius kernels reduces to the study of irreducible representations of the first Frobenius kernel. In the preceding paper in this series, deforming the distribution algebra of a higher Frobenius kernel yielded a family of deformations called higher reduced enveloping algebras. In this paper, we prove that the Steinberg decomposition can be similarly deformed, allowing us to reduce representation theoretic questions about these algebras to questions about reduced enveloping algebras. We use this to derive structural results about modules over these algebras. Separately, we also show that many of the results in the preceding paper hold without an assumption of reductivity.

scholarly journals Second cohomology groups for Frobenius kernels and related structures

2007 ◽  
Vol 209 (1) ◽  
pp. 162-197 ◽  
Author(s):  
Christopher P. Bendel ◽  
Daniel K. Nakano ◽  
Cornelius Pillen
Keyword(s):  
Cohomology Groups ◽  
Frobenius Kernels

scholarly journals On comparing the cohomology of algebraic groups, finite Chevalley groups and Frobenius kernels

2001 ◽  
Vol 163 (2) ◽  
pp. 119-146 ◽  
Author(s):  
Christopher P. Bendel ◽  
Daniel K. Nakano ◽  
Cornelius Pillen
Keyword(s):  
Algebraic Groups ◽  
Chevalley Groups ◽  
Frobenius Kernels

scholarly journals Bounding Cohomology for Finite Groups and Frobenius Kernels

2015 ◽  
Vol 18 (3) ◽  
pp. 739-760 ◽  
Author(s):  
Christopher P. Bendel ◽  
Daniel K. Nakano ◽  
Brian J. Parshall ◽  
Cornelius Pillen ◽  
Leonard L. Scott ◽  
...  
Keyword(s):  
Finite Groups ◽  
Frobenius Kernels
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