Derivations from the even parts into the odd parts for Lie superalgebras W and S

Abstract

Let $\mathcal{W}$ and $\mathcal{S}$ denote the even parts of the general Witt superalgebra $W$ and the special superalgebra $S$ over a field of characteristic $p>3,$ respectively. In this note, using the method of reduction on $\mathbb{Z}$-gradations, we determine the derivation space $\mathrm{Der}(\mathcal{W},W_{\bar{1}})$ from $\mathcal{W}$ into $W_{\bar{1}}$ and the derivation space $\mathrm{Der}(\mathcal{S},W_{\bar{1}})$ from $\mathcal{S}$ into $W_{\bar{1}}.$ In particular, the derivation space $\mathrm{Der}(\mathcal{S},S_{\bar{1}})$ is determined.

19 pages

References in corpus (1)

• Derivations for the even parts of modular Lie superalgebras $W$ and $S$ of Cartan type