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    Rights statement: The final, definitive version of this article has been published in the Journal, Journal of Algebra 389, 2013, © ELSEVIER.

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KW-sections for Vinberg's θ-groups of exceptional type

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KW-sections for Vinberg's θ-groups of exceptional type. / Levy, Paul.
In: Journal of Algebra, Vol. 389, 01.09.2013, p. 78-97.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Levy, P 2013, 'KW-sections for Vinberg's θ-groups of exceptional type', Journal of Algebra, vol. 389, pp. 78-97. https://doi.org/10.1016/j.jalgebra.2013.04.035

APA

Levy, P. (2013). KW-sections for Vinberg's θ-groups of exceptional type. Journal of Algebra, 389, 78-97. https://doi.org/10.1016/j.jalgebra.2013.04.035

Vancouver

Levy P. KW-sections for Vinberg's θ-groups of exceptional type. Journal of Algebra. 2013 Sept 1;389:78-97. doi: 10.1016/j.jalgebra.2013.04.035

Author

Levy, Paul. / KW-sections for Vinberg's θ-groups of exceptional type. In: Journal of Algebra. 2013 ; Vol. 389. pp. 78-97.

Bibtex

@article{fcb55b23a4f8431196f53b31c3d29439,
title = "KW-sections for Vinberg's θ-groups of exceptional type",
abstract = "Let k be an algebraically closed field of characteristic not equal to 2 or 3, let G be an almost simple algebraic group of type F4, G2 or D4 and let \theta be an automorphism of G of finite order, coprime to the characteristic. In this paper we consider the \theta-group (in the sense of Vinberg) associated to these choices; we classify the positive rank automorphisms via Kac diagrams and we describe the little Weyl group in each case. As a result we show that all -groups in types G2, F4 and D4 have KW-sections, confirming a conjecture of Popov in these cases.",
keywords = "Algebraic groups, Lie algebras, Automorphisms, Invariant theory, Pseudo-reflection groups",
author = "Paul Levy",
note = "The final, definitive version of this article has been published in the Journal, Journal of Algebra 389, 2013, {\textcopyright} ELSEVIER.",
year = "2013",
month = sep,
day = "1",
doi = "10.1016/j.jalgebra.2013.04.035",
language = "English",
volume = "389",
pages = "78--97",
journal = "Journal of Algebra",
issn = "0021-8693",
publisher = "ELSEVIER ACADEMIC PRESS INC",

}

RIS

TY - JOUR

T1 - KW-sections for Vinberg's θ-groups of exceptional type

AU - Levy, Paul

N1 - The final, definitive version of this article has been published in the Journal, Journal of Algebra 389, 2013, © ELSEVIER.

PY - 2013/9/1

Y1 - 2013/9/1

N2 - Let k be an algebraically closed field of characteristic not equal to 2 or 3, let G be an almost simple algebraic group of type F4, G2 or D4 and let \theta be an automorphism of G of finite order, coprime to the characteristic. In this paper we consider the \theta-group (in the sense of Vinberg) associated to these choices; we classify the positive rank automorphisms via Kac diagrams and we describe the little Weyl group in each case. As a result we show that all -groups in types G2, F4 and D4 have KW-sections, confirming a conjecture of Popov in these cases.

AB - Let k be an algebraically closed field of characteristic not equal to 2 or 3, let G be an almost simple algebraic group of type F4, G2 or D4 and let \theta be an automorphism of G of finite order, coprime to the characteristic. In this paper we consider the \theta-group (in the sense of Vinberg) associated to these choices; we classify the positive rank automorphisms via Kac diagrams and we describe the little Weyl group in each case. As a result we show that all -groups in types G2, F4 and D4 have KW-sections, confirming a conjecture of Popov in these cases.

KW - Algebraic groups

KW - Lie algebras

KW - Automorphisms

KW - Invariant theory

KW - Pseudo-reflection groups

U2 - 10.1016/j.jalgebra.2013.04.035

DO - 10.1016/j.jalgebra.2013.04.035

M3 - Journal article

VL - 389

SP - 78

EP - 97

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

ER -