On some almost quadratic algebras coming from twisted derivations
(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)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/386678
- author
- Larsson, Daniel LU ; Sigurdsson, Gunnar and Silvestrov, Sergei LU
- organization
- publishing date
- 2006
- 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
- 2022-01-28 21:55:55
@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}},
keywords = {{twisted Jacobi; extensions; sigma-derivations; quasi-deformation; colour Lie algebras; quasi-hom-Lie algebras; hom-Lie algebras; identities; almost quadratic algebras.}},
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}},
}