Journal of Lie Theory

no. 3
Derivations from the Even Parts into the Odd Parts for Lie Superalgebras W and S
Wende Liu1; Baoling Guan2, 3
1Dept. of Mathematics, Harbin Normal University, Harbin 150080, P. R. China
2(1) Dept. of Mathematics, Harbin Normal University, Harbin 150080, P. R. China
3(2) Dept. of Mathematics, Qiqihar University, Qiqihar 161006, P. R. China
Journal of Lie Theory, Volume 17 (2007) no. 3, pp. 449-468
\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.
DOI: 10.5802/jolt.455
Classification: 17B50, 17B40
Keywords: Generalized Witt superalgebra, special superalgebra, derivation space, canonical torus

Wende Liu  1 ; Baoling Guan  2 , 3

1 Dept. of Mathematics, Harbin Normal University, Harbin 150080, P. R. China
2 (1) Dept. of Mathematics, Harbin Normal University, Harbin 150080, P. R. China
3 (2) Dept. of Mathematics, Qiqihar University, Qiqihar 161006, P. R. China 
Wende Liu; Baoling Guan. Derivations from the Even Parts into the Odd Parts for Lie Superalgebras W and S. Journal of Lie Theory, Volume 17 (2007) no. 3, pp. 449-468. doi: 10.5802/jolt.455
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     title = {Derivations from the {Even} {Parts} into the {Odd} {Parts} for {Lie} {Superalgebras} {W} and {S}},
     journal = {Journal of Lie Theory},
     pages = {449--468},
     year = {2007},
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     doi = {10.5802/jolt.455},
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