Derivations from the Even Parts into the Odd Parts for Lie Superalgebras W and S

W. Liu ; B. Guan

Journal of Lie theory, Tome 17 (2007) no. 3, pp. 449-468.

Résumé

\def\Z{{\mathbb Z}\,} \def\Der{\mathop{\rm Der\,}\nolimits} Let $\cal W$ and $\cal S$ denote the even parts of the generalized 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 $\Z$-gradations, we determine the derivation space $\Der( {\cal W}, W_{\overline1})$ from $\cal W$ into $W_{\overline1}$ and the derivation space $\Der({\cal S}, W_{\overline1})$ from $\cal S$ into $W_{\overline1}$. In particular, the derivation space $\Der({\cal S}, S_{\overline1})$ is determined.

Détail

Classification : 17B50, 17B40
Mots-clés : Generalized Witt superalgebra, special superalgebra, derivation space, canonical torus