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On some almost quad...
On some almost quadratic algebras coming from twisted derivations
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Larsson, Daniel (author)
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- Sigurdsson, Gunnar (author)
- KTH,Teoretisk fysik
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Silvestrov, Sergei D. (author)
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(creator_code:org_t)
- 2006
- 2006
- English.
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In: Journal of Nonlinear Mathematical Physics. - 1402-9251 .- 1776-0852. ; 13, s. 76-86
- Related links:
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https://urn.kb.se/re...
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https://doi.org/10.2...
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Abstract
Subject headings
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- 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.
Subject headings
- NATURVETENSKAP -- Fysik (hsv//swe)
- NATURAL SCIENCES -- Physical Sciences (hsv//eng)
Keyword
- quasi-hom-Lie algebras
- hom-Lie algebras
- colour Lie algebras
- quasi-deformation
- sigma-derivations
- extensions
- twisted Jacobi identities
- almost quadratic algebras.
Publication and Content Type
- ref (subject category)
- art (subject category)
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