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Lie algebras with triality

โœ Scribed by Alexander Grishkov

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
220 KB
Volume
266
Category
Article
ISSN
0021-8693

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โœฆ Synopsis

By analogy with the definition of group with triality we introduce Lie algebra with triality as Lie algebra L which admits the group of automorphisms S 3 = {ฯƒ, ฯ | ฯƒ 2 = ฯ 3 = 1, ฯƒฯฯƒ = ฯ 2 } such that for any x โˆˆ L we have (x ฯƒx) + (x ฯƒx) ฯ + (x ฯƒx) ฯ 2 = 0. We describe the structure of finite-dimensional Lie algebra with triality over a field of characteristic 0 and give applications of Lie algebras with triality to the theory of Malcev algebras.

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