Quasi-Deformations of 𝔰𝔩2(𝔽) Using Twisted Derivations

By Daniel S. D. Larsson, Sergei Silvestrov. 2005

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In this article we apply a method devised in Hartwig, Larsson, and Silvestrov (2006) and Larsson and Silvestrov (2005a) 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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/caab9dd40f9faaf7ec2ccf017fa572fa2a4b52fe

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In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Notes on 1-parameter formal deformations of Hom-associative and Hom-Lie algebras (2010, methodology): “This family of Hom-Lie algebras was constructed in [24] using a quasi-deformation scheme based on discretizing by means of Jackson q-derivations a representation of sl2(K) by one-dimensional vector fields (first order ordinary differential operators) and using the twisted commutator bracket defined ”