Quasi-Deformations of sl2(F) Using Twisted Derivations
Silvestrov, Sergei; Larsson, Daniel (2007). Quasi-Deformations of sl2(F) Using Twisted Derivations. Communications in Algebra, 35, (12), 4303 - 4318
|
Published
|
English
Authors:
Silvestrov, Sergei
;
Larsson, Daniel
Department:
Mathematics (Faculty of Engineering)
Non-commutative Geometry-lup-obsolete
Project:
Non-commutative Analysis of Dynamics, Fractals and Wavelets
Non-commutative Geometry in Mathematics and Physics
Research Group:
Non-commutative Geometry-lup-obsolete
Abstract:
In this article we apply a method devised in Hartwig, Larsson, and Silvestrov (2006) and Larsson and Silvestrov (2005a) to the simple 3-dimensional Lie algebra sl2(F). One of the main points of this deformation method is that the deformed algebra comes endowed with a canonical twisted Jacobi identity. We show in the present article that when our deformation scheme is applied to sl2(F) we can, by choosing parameters suitably, deform sl2(F) into the Heisenberg Lie algebra and some other 3-dimensional Lie algebras in addition to more exotic types of algebras, this being in stark contrast to the classical deformation schemes where sl2(F) is rigid.
Keywords:
Twisted derivation ;
Quasi-deformations ;
Twisted Jacobi identity ;
Quasi-Lie algebras
Cite this