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Izv. Akad. Nauk SSSR Ser. Mat., 1976, Volume 40, Issue 3, Pages 488–526 (Mi izv2123)  

This article is cited in 46 scientific papers (total in 47 papers)

The Weyl group of a graded Lie algebra

È. B. Vinberg


Abstract: The action of the group $G_0$ of fixed points of a semisimple automorphism $\theta$ of a reductive algebraic group $G$ on an eigenspace $V$ of this automorphism in the Lie algebra $\mathfrak g$ of the group $G$ is considered. The linear groups which are obtained in this manner are called $\theta$-groups in this paper; they have certain properties which are analogous to properties of the adjoint group. In particular, the notions of Cartan subgroup and Weyl group can be introduced for $\theta$-groups. It is shown that the Weyl group is generated by complex reflections; from this it follows that the algebra of invariants of any $\theta$-group is free.
Bibliography: 30 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1976, 10:3, 463–495

Bibliographic databases:

UDC: 519.4
MSC: Primary 17B05; Secondary 20G20, 17B10, 17B20, 17B25, 17B45, 17B65
Received: 17.01.1975

Citation: È. B. Vinberg, “The Weyl group of a graded Lie algebra”, Izv. Akad. Nauk SSSR Ser. Mat., 40:3 (1976), 488–526; Math. USSR-Izv., 10:3 (1976), 463–495

Citation in format AMSBIB
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\by \`E.~B.~Vinberg
\paper The Weyl group of a~graded Lie algebra
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1976
\vol 40
\issue 3
\pages 488--526
\mathnet{http://mi.mathnet.ru/izv2123}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=430168}
\zmath{https://zbmath.org/?q=an:0363.20035}
\transl
\jour Math. USSR-Izv.
\yr 1976
\vol 10
\issue 3
\pages 463--495
\crossref{https://doi.org/10.1070/IM1976v010n03ABEH001711}


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