On Some Almost Quadratic Algebras Coming from Twisted Derivations
- 10.2991/jnmp.2006.13.s.9How to use a DOI?
- quasi-hom-Lie algebras, hom-Lie algebras, colour Lie algebras, quasideformation, -derivations, extensions, twisted Jacobi identities, almost quadratic algebras.
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.
- © 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/).
Cite this article
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 -