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arXiv · 0905.2599

Twisted cocycles of Lie algebras and corresponding invariant functions

Jiri Hrivnak·Petr Novotny
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Abstract

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 one-parametric nilpotent continua of Lie algebras. These functions also provide necessary criteria for existence of 1-parametric continuous contraction.

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Jiri Hrivnak, Petr Novotny. 2009-05-15. Twisted cocycles of Lie algebras and corresponding invariant functions. https://doi.org/10.1016/j.laa.2008.11.003

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