Twisted cocycles of Lie algebras and corresponding invariant functions

Details Twisted cocycles of Lie algebras and corresponding invariant functions Twisted cocycles of Lie algebras and corresponding invariant functions

2009-05-15

arxiv.org/abs/0905.2599v1

Linear Algebra and its Applications 430 (2009) 1384-1403

Physics

Mathematical Physics

19 pages

Scientific paper

10.1016/j.laa.2008.11.003

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 $(\alpha,\beta,\gamma)$--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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