Journal of Nonlinear Mathematical Physics

Volume 13, Issue Supplement, August 2006, Pages 76 - 87

On Some Almost Quadratic Algebras Coming from Twisted Derivations

Authors
Daniel LARSSON, Gunnar SIGURDSSON, Sergei D SILVESTROV
Corresponding Author
Daniel LARSSON
Available Online 27 November 2006.
DOI
https://doi.org/10.2991/jnmp.2006.13.s.9How to use a DOI?
Keywords
quasi-hom-Lie algebras, hom-Lie algebras, colour Lie algebras, quasideformation, -derivations, extensions, twisted Jacobi identities, almost quadratic algebras.
Abstract
This paper explores the quasi-deformation scheme devised in [1, 3] as applied to the simple Lie algebra sl2(F) for specific choices of the involved parameters and underlying algebras. One of the main points of this method is that the quasi-deformed algebra comes endowed with a canonical twisted Jacobi identity. We show in the present article that when the quasi-deformation method is applied to sl2(F) one obtains multiparameter families of almost quadratic algebras, and by choosing parameters suitably, sl2(F) is quasi-deformed into three-dimensional and four-dimensional Lie algebras and algebras closely resembling Lie superalgebras and colour Lie algebras, this being in stark contrast to the classical deformation schemes where sl2(F) is rigid.
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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
13 - 100
Pages
76 - 87
Publication Date
2006/11
ISBN
91-974824-6-3
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.2991/jnmp.2006.13.s.9How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - JOUR
AU  - Daniel LARSSON
AU  - Gunnar SIGURDSSON
AU  - Sergei D SILVESTROV
PY  - 2006
DA  - 2006/11
TI  - On Some Almost Quadratic Algebras Coming from Twisted Derivations
JO  - Journal of Nonlinear Mathematical Physics
SP  - 76
EP  - 87
VL  - 13
IS  - Supplement
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2006.13.s.9
DO  - https://doi.org/10.2991/jnmp.2006.13.s.9
ID  - LARSSON2006
ER  -