1. Double Derivations of n-Lie Superalgebras
- Author
-
Liangyun Chen, Xin Zhou, and Bing Sun
- Subjects
Pure mathematics ,Algebra and Number Theory ,Applied Mathematics ,010102 general mathematics ,Lie superalgebra ,010103 numerical & computational mathematics ,01 natural sciences ,Superalgebra ,Set (abstract data type) ,Mathematics::Quantum Algebra ,Derivation ,0101 mathematics ,Algebra over a field ,Mathematics::Representation Theory ,Mathematics - Abstract
Let 𝔤 be an n-Lie superalgebra. We study the double derivation algebra [Formula: see text] and describe the relation between [Formula: see text] and the usual derivation Lie superalgebra Der(𝔤). We show that the set [Formula: see text] of all double derivations is a subalgebra of the general linear Lie superalgebra gl(𝔤) and the inner derivation algebra ad(𝔤) is an ideal of [Formula: see text]. We also show that if 𝔤 is a perfect n-Lie superalgebra with certain constraints on the base field, then the centralizer of ad(𝔤) in [Formula: see text] is trivial. Finally, we give that for every perfect n-Lie superalgebra 𝔤, the triple derivations of the derivation algebra Der(𝔤) are exactly the derivations of Der(𝔤).
- Published
- 2018