Journal of Lie Theory 17 (2007), No. 3, 449--468
Copyright Heldermann Verlag 2007
Derivations from the Even Parts into the Odd Parts for Lie Superalgebras W and S
Wende Liu
Dept. of Mathematics, Harbin Normal University, Harbin 150080, P. R. China
wendeliu@hrbnu.edu.cn
Baoling Guan
(1) Dept. of Mathematics, Harbin Normal University, Harbin 150080, P. R. China
(2) Dept. of Mathematics, Qiqihar University, Qiqihar 161006, P. R. China
[Abstract-pdf]
\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.
Keywords: Generalized Witt superalgebra, special superalgebra, derivation space, canonical torus.
MSC: 17B50, 17B40
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