Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1894095 | Journal of Geometry and Physics | 2010 | 9 Pages |
Abstract
We obtain a realization of the Lie superalgebra D(2,1;α)D(2,1;α) in differential operators on the supercircle S1|2S1|2 and in 4×4 matrices over a Weyl algebra. A contraction of D(2,1;α)D(2,1;α) is isomorphic to the universal central extension pslˆ(2|2) of psl(2|2)psl(2|2). We realize it in 4×4 matrices over the associative algebra of pseudodifferential operators on S1S1. Correspondingly, there exists a three-parameter family of irreducible representations of pslˆ(2|2) in a (2|2)(2|2)-dimensional complex superspace.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
Elena Poletaeva,