Journal of Lie Theory

no. 3
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
\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 
@article{JOLT_2007_17_3_a0,
     author = {W. Liu and B. Guan},
     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},
     volume = {17},
     number = {3},
     doi = {10.5802/jolt.455},
     zbl = {1161.17010},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.455/}
}
TY  - JOUR
AU  - W. Liu
AU  - B. Guan
TI  - Derivations from the Even Parts into the Odd Parts for Lie Superalgebras W and S
JO  - Journal of Lie Theory
PY  - 2007
SP  - 449
EP  - 468
VL  - 17
IS  - 3
UR  - https://jolt.centre-mersenne.org/articles/10.5802/jolt.455/
DO  - 10.5802/jolt.455
ID  - JOLT_2007_17_3_a0
ER  - 
%0 Journal Article
%A W. Liu
%A B. Guan
%T Derivations from the Even Parts into the Odd Parts for Lie Superalgebras W and S
%J Journal of Lie Theory
%D 2007
%P 449-468
%V 17
%N 3
%U https://jolt.centre-mersenne.org/articles/10.5802/jolt.455/
%R 10.5802/jolt.455
%F JOLT_2007_17_3_a0
W. Liu; B. 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

Cited by Sources: