Varieties of nilpotent elements for simple Lie algebras I: Good primes

David John Benson; B. D. Boe; D. K. Nakano; Nadia Mazza; UGA VIGRE Algebra Group

doi:10.1016/j.jalgebra.2004.05.023

Varieties of nilpotent elements for simple Lie algebras I: Good primes

David John Benson, B. D. Boe, D. K. Nakano, Nadia Mazza, UGA VIGRE Algebra Group

Mathematical Science

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

Abstract

Let G be a simple algebraic group over k = C, or F-p where p is good. Set g = Lie G. Given r is an element of N and a faithful (restricted) representation rho: g --> gl(V), one can define a variety of nilpotent elements N-r,(rho)(g) = {x is an element of g: rho(x)(r) = 0}. In this paper we determine this variety when rho is an irreducible representation of minimal dimension or the adjoint representation. (C) 2004 Elsevier Inc. All rights reserved.

Original language	English
Pages (from-to)	719-737
Number of pages	18
Journal	Journal of Algebra
Volume	280
Issue number	2
DOIs	https://doi.org/10.1016/j.jalgebra.2004.05.023
Publication status	Published - 2004

Keywords

SUPPORT VARIETIES
UNIPOTENT ELEMENTS
COHOMOLOGY

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10.1016/j.jalgebra.2004.05.023

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abstract = "Let G be a simple algebraic group over k = C, or F-p where p is good. Set g = Lie G. Given r is an element of N and a faithful (restricted) representation rho: g --> gl(V), one can define a variety of nilpotent elements N-r,(rho)(g) = {x is an element of g: rho(x)(r) = 0}. In this paper we determine this variety when rho is an irreducible representation of minimal dimension or the adjoint representation. (C) 2004 Elsevier Inc. All rights reserved.",

keywords = "SUPPORT VARIETIES, UNIPOTENT ELEMENTS, COHOMOLOGY",

author = "Benson, {David John} and Boe, {B. D.} and Nakano, {D. K.} and Nadia Mazza and {UGA VIGRE Algebra Group}",

year = "2004",

doi = "10.1016/j.jalgebra.2004.05.023",

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journal = "Journal of Algebra",

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T1 - Varieties of nilpotent elements for simple Lie algebras I: Good primes

AU - Benson, David John

AU - Boe, B. D.

AU - Nakano, D. K.

AU - Mazza, Nadia

AU - UGA VIGRE Algebra Group

PY - 2004

Y1 - 2004

N2 - Let G be a simple algebraic group over k = C, or F-p where p is good. Set g = Lie G. Given r is an element of N and a faithful (restricted) representation rho: g --> gl(V), one can define a variety of nilpotent elements N-r,(rho)(g) = {x is an element of g: rho(x)(r) = 0}. In this paper we determine this variety when rho is an irreducible representation of minimal dimension or the adjoint representation. (C) 2004 Elsevier Inc. All rights reserved.

AB - Let G be a simple algebraic group over k = C, or F-p where p is good. Set g = Lie G. Given r is an element of N and a faithful (restricted) representation rho: g --> gl(V), one can define a variety of nilpotent elements N-r,(rho)(g) = {x is an element of g: rho(x)(r) = 0}. In this paper we determine this variety when rho is an irreducible representation of minimal dimension or the adjoint representation. (C) 2004 Elsevier Inc. All rights reserved.

KW - SUPPORT VARIETIES

KW - UNIPOTENT ELEMENTS

KW - COHOMOLOGY

U2 - 10.1016/j.jalgebra.2004.05.023

DO - 10.1016/j.jalgebra.2004.05.023

M3 - Article

SN - 0021-8693

VL - 280

SP - 719

EP - 737

JO - Journal of Algebra

JF - Journal of Algebra

IS - 2

ER -

Varieties of nilpotent elements for simple Lie algebras I: Good primes

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Keywords

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