Deformations of Lie algebras using σ-derivations

• DOI: 10.1016/j.jalgebra.2005.07.036
• Publication Date: 2005-12-22T23:18:40Z
• Authors: Jonas T. Hartwig; Daniel Larsson; Sergei D. Silvestrov
• Keywords: Jacobi identity

52 pages<br/>In this article we develop an approach to deformations of the Witt and Virasoro algebras based on $��$-derivations. We show that $��$-twisted Jacobi type identity holds for generators of such deformations. For the $��$-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.<br/>