On the Cohomology and Extensions of First-Class n-Lie Superalgebras

Abstract

An n-Lie superalgebra of parity 0 is called a first-class n-Lie superalgebra. In this paper, we give the representation and cohomology for a first-class n-Lie superalgebra and obtain a relation between extensions of a first-class n-Lie superalgebra 𝔟 by an abelian one 𝔞 and . We also introduce the notion of T*-extensions of first-class n-Lie superalgebras and prove that every finite-dimensional nilpotent metric first-class n-Lie superalgebra (𝔤, ⟨,⟩_𝔤) over an algebraically closed field of characteristic not 2 is isometric to a suitable T*-extension.

Key Words:

• Cohomology
• Extension
• n-Lie superalgebra

2010 Mathematics Subject Classification:

• 16S70
• 17A42
• 17B56
• 17B70

ACKNOWLEDGMENTS

The authors would like to thank the referee for valuable comments and suggestions on this article.

Notes

Communicated by M. Bresar.