Quasi-Deformations of 𝔰𝔩2(𝔽) Using Twisted Derivations |
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Authors: | Daniel Larsson |
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Institution: | Department of Mathematics , Uppsala Univeristy , Uppsala, Sweden |
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Abstract: | In this article we apply a method devised in Hartwig, Larsson, and Silvestrov (2006
Hartwig , J. T. ,
Larsson , D. ,
Silvestrov , S. D. ( 2006 ). Deformations of Lie algebras using σ-derivations . J. Algebra 295 : 314 – 361 .Crossref], Web of Science ®] , Google Scholar]) and Larsson and Silvestrov (2005a
Larsson , D. ,
Silvestrov , S. D. (2005a). Quasi-hom-Lie algebras, Central extensions and 2-cocycle-like identities. J. Algebra 288:321–344.Crossref], Web of Science ®] , Google Scholar]) to the simple 3-dimensional Lie algebra 𝔰𝔩2(𝔽). One of the main points of this deformation method is that the deformed algebra comes endowed with a canonical twisted Jacobi identity. We show in the present article that when our deformation scheme is applied to 𝔰𝔩2(𝔽) we can, by choosing parameters suitably, deform 𝔰𝔩2(𝔽) into the Heisenberg Lie algebra and some other 3-dimensional Lie algebras in addition to more exotic types of algebras, this being in stark contrast to the classical deformation schemes where 𝔰𝔩2(𝔽) is rigid. |
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Keywords: | Quasi-deformations Quasi-Lie algebras Twisted derivation Twisted Jacobi identity |
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