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Deformations of Lie algebras using σ-derivations

2005; Elsevier BV; Volume: 295; Issue: 2 Linguagem: Inglês

10.1016/j.jalgebra.2005.07.036

1090-266X

Jonas T. Hartwig, Daniel Larsson, Sergei Silvestrov,

Nonlinear Waves and Solitons

In this article we develop an approach to deformations of the Witt and Virasoro algebras based on σ-derivations. We show that σ-twisted Jacobi type identity holds for generators of such deformations. For the σ-twisted generalization of Lie algebras modeled by this construction, we develop a theory of central extensions. We show that our approach can be used to construct new deformations of Lie algebras and their central extensions, which in particular include naturally the q-deformations of the Witt and Virasoro algebras associated to q-difference operators, providing also corresponding q-deformed Jacobi identities.