On matrix realizations of the Lie superalgebra D(2, 1; α)

JOURNAL OF GEOMETRY AND PHYSICS

卷:60

Article

Poletaeva, Elena

关键词: Contraction;    Poisson superalgebra;    Differential operators;    Weyl algebra;   

DOI  :  10.1016/j.geomphys.2010.06.008

来源: Elsevier

【 摘 要 】

We obtain a realization of the Lie superalgebra D(2, 1: alpha) in differential operators on the supercircle S-1/2 and in 4 x 4 matrices over a Weyl algebra. A contraction of D(2, 1: alpha) is isomorphic to the universal central extension psl(2 vertical bar 2) of psi(2 vertical bar 2). We realize it in 4 x 4 matrices over the associative algebra of pseudodifferential operators on S'. Correspondingly, there exists a three-parameter family of irreducible representations of psl(2 vertical bar 2) in a (2 vertical bar 2)-dimensional complex superspace. (c) 2010 Elsevier B.V. All rights reserved.

【 授权许可】

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