On Some Almost Quadratic Algebras Coming from Twisted Derivations

DOI

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.

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Daniel Larsson
AU  - Gunnar Sigurdsson
AU  - Sergei D. Silvestrov
PY  - 2006
DA  - 2006/08/01
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  - 10.2991/jnmp.2006.13.s.9
ID  - Larsson2006
ER  -