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Transactions of the Moscow Mathematical Society

ISSN 1547-738X(online) ISSN 0077-1554(print)



The semisimple subalgebras of exceptional Lie algebras

Author: A. N. Minchenko
Translated by: E. Khukhro
Original publication: Trudy Moskovskogo Matematicheskogo Obshchestva, tom 67 (2006).
Journal: Trans. Moscow Math. Soc. 2006, 225-259
MSC (2000): Primary 17B25; Secondary 17B20, 22E10
Published electronically: December 27, 2006
MathSciNet review: 2301595
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Abstract: Dynkin classified the maximal semisimple subalgebras of exceptional Lie algebras up to conjugacy, but only classified the simple subalgebras up to the coarser relation of linear conjugacy. In the present paper the simple subalgebras of exceptional Lie algebras are classified up to conjugacy, and their normalizers in the group are found. In a certain sense, this completes the description of the semisimple subalgebras of semisimple Lie algebras. As a by-product we obtain a list of all those semisimple subalgebras of exceptional Lie algebras for which the linear conjugacy class does not coincide with their conjugacy class (in the classical case the corresponding result was known).

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Additional Information

A. N. Minchenko
Affiliation: Mechanics and Mathematics Department, Moscow State University, Leninskie Gory, Moscow, GSP-2, 119992, Russia

Keywords: Exceptional Lie algebras, semisimple subalgebra, adjoint group, simple subalgebra, semisimple embedding, simple embedding, conjugacy class, normalizer
Published electronically: December 27, 2006
Article copyright: © Copyright 2006 American Mathematical Society