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On some almost quadratic algebras coming from twisted derivations

Larsson, Daniel LU ; Sigurdsson, Gunnar and Silvestrov, Sergei LU (2006) In Journal of Nonlinear Mathematical Physics 13. p.76-86
Abstract
This paper explores the quasi-deformation scheme devised in [1, 3] as applied to the simple Lie algebra sl(2)(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 sl(2)(F) one obtains multiparameter families of almost quadratic algebras, and by choosing parameters suitably, sl(2)(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... (More)
This paper explores the quasi-deformation scheme devised in [1, 3] as applied to the simple Lie algebra sl(2)(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 sl(2)(F) one obtains multiparameter families of almost quadratic algebras, and by choosing parameters suitably, sl(2)(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 sl(2)(F) is rigid. (Less)
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author
; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
twisted Jacobi, extensions, sigma-derivations, quasi-deformation, colour Lie algebras, quasi-hom-Lie algebras, hom-Lie algebras, identities, almost quadratic algebras.
in
Journal of Nonlinear Mathematical Physics
volume
13
pages
76 - 86
publisher
Taylor & Francis
external identifiers
  • wos:000241392500010
  • scopus:33747686517
ISSN
1402-9251
DOI
10.2991/jnmp.2006.13.s.9
language
English
LU publication?
yes
id
243147d7-7c7f-4a81-82a0-131ab41d95f9 (old id 386678)
date added to LUP
2016-04-01 16:45:37
date last changed
2021-06-23 03:05:57
@article{243147d7-7c7f-4a81-82a0-131ab41d95f9,
  abstract     = {This paper explores the quasi-deformation scheme devised in [1, 3] as applied to the simple Lie algebra sl(2)(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 sl(2)(F) one obtains multiparameter families of almost quadratic algebras, and by choosing parameters suitably, sl(2)(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 sl(2)(F) is rigid.},
  author       = {Larsson, Daniel and Sigurdsson, Gunnar and Silvestrov, Sergei},
  issn         = {1402-9251},
  language     = {eng},
  pages        = {76--86},
  publisher    = {Taylor & Francis},
  series       = {Journal of Nonlinear Mathematical Physics},
  title        = {On some almost quadratic algebras coming from twisted derivations},
  url          = {http://dx.doi.org/10.2991/jnmp.2006.13.s.9},
  doi          = {10.2991/jnmp.2006.13.s.9},
  volume       = {13},
  year         = {2006},
}