Low Dimensional Homology Groups of the Orthosymplectic Lie Superalgebra $\osp(1,2)$

Guy Roger Biyogmam

Abstract

We realize the Lie superalgebra $\osp(1,2)$ in terms of first order differential operators and endow it with the Lie superbracket of vector fields to determine the basis (co)cycles of low dimensional (co)homology groups of $\osp(1,2)$ with trivial coefficients, using the complex introduced by Tanaka \cite{T}. Our calculations agree with the result obtained by Fuks and Leites.

Keywords

Lie superalgebras, Homology of Lie superalgebras.

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