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
Download:
DOI:
| Published | 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
ISSN:
0021-8693
LUP-ID:
de6109b3-2340-4347-bed3-6f15455c23e2 | Link: https://lup.lub.lu.se/record/de6109b3-2340-4347-bed3-6f15455c23e2 | Statistics

Cite this