Deformations of Lie Algebras using σ-Derivations
Hartwig, Jonas; Larsson, Daniel; Silvestrov, Sergei (2006). Deformations of Lie Algebras using σ-Derivations. Journal of Algebra, 295, (2), 314 - 361
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Published
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English
Authors:
Hartwig, Jonas
;
Larsson, Daniel
;
Silvestrov, Sergei
Department:
Mathematics (Faculty of Engineering)
Non-commutative Geometry-lup-obsolete
Research Group:
Non-commutative Geometry-lup-obsolete
Abstract:
In this article we develop an approach to deformations of the Witt and Virasoro algebras based on sigma-derivations. We show that sigma-twisted Jacobi type identity holds for generators of such deformations. For the sigma-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. (c) 2005 Elsevier Inc. All rights reserved.
Keywords:
q-Witt algebras ;
q-Virasoro algebras ;
Jacobi ;
type identities ;
Lie algebras ;
sigma-derivations ;
extensions ;
deformation theory
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