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Twisted cocycles of lie algebras and corresponding invariant functions

✍ Scribed by Jiřı´ Hrivnák; Petr Novotný

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
251 KB
Volume
430
Category
Article
ISSN
0024-3795

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✦ Synopsis

We consider finite-dimensional complex Lie algebras. Using certain complex parameters we generalize the concept of cohomology cocycles of Lie algebras. A special case is generalization of 1-cocycles with respect to the adjoint representation -so called (α, β, γ )-derivations. Parametric sets of spaces of cocycles allow us to define complex functions which are invariant under Lie isomorphisms. Such complex functions thus represent useful invariants -we show how they classify three and four-dimensional Lie algebras as well as how they apply to some eight-dimensional 1-parametric nilpotent continua of Lie algebras. These functions also provide necessary criteria for existence of 1-parametric continuous contraction.

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