QUASI-REDUCTIVE (BI)PARABOLIC SUBALGEBRASIN REDUCTIVE LIE ALGEBRAS

Karin BAUR; Anne MOREAU

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QUASI-REDUCTIVE (BI)PARABOLIC SUBALGEBRASIN REDUCTIVE LIE ALGEBRAS

机译：QUASI-REDUCTIVE (BI)PARABOLIC SUBALGEBRASIN REDUCTIVE LIE ALGEBRAS

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We say that a finite dimensional Lie algebra is quasi-reductive if it has a linear form whose stabilizer for the coadjoint representation, modulo the center, is a reductive Lie algebra with a center consisting of semisimple elements. Parabolic subalgebras of a semisimple Lie algebra are not always quasi-reductive (except in types A or C by work of Panyushev). The classification of quasi-reductive parabolic subalgebras in the classical case has been recently achieved in unpub-lished work of Duflo, Khalgui and Torasso. In this paper, we investigate the quasi-reductivity of biparabolic subalgebras of reductive Lie algebras. Biparabolic (or seaweed) subalgebras are the intersection of two parabolic subalgebras whose sum is the total Lie algebra. As a main result, we complete the classification of quasi-reductive parabolic subalgebras of reductive Lie algebras by considering the excep-tional cases.

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《Annales de l'Institut Fourier》 |2011年第2期|417-451|共35页
作者
Karin BAUR; Anne MOREAU;
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作者单位

ETH Zurich Departement Mathematik Rdmistrasse 101 8092 Zurich (Switzerland);

LMA Boulevard Marie et Pierre Curie 86962 Futuroscope Chasseneuil Cedex (France);

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正文语种英语
中图分类自然科学总论;
关键词
Reductive Lie algebras; quasi-reductive Lie algebras; index; biparabolic Lie algebras; seaweed algebras; regular linear forms;

QUASI-REDUCTIVE (BI)PARABOLIC SUBALGEBRASIN REDUCTIVE LIE ALGEBRAS

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