Derivation Algebra Der(H) and Central Extensions of Lie Superalgebras

Abstract

In this paper, we obtain the Lie superalgebra of superderivations of H type Lie superalgebra and discuss the relation between skew superderivations space SkDer(L) and central extension H ²(L, F) on some Lie superalgebra L. As an application, we obtain the dimension of central extension of Lie superalgebras with a nondegenerate associative forms.

Key Words:

• Derivation algebra
• Central extensions
• Lie superalgebra

Mathematics Subject Classification:

• 17B40
• 17B56

Acknowledgments