Super-biderivations of the contact Lie superalgebra K(m,n;t¯)

Abstract

Let K denote the contact Lie superalgebra $K(m,n;\underset{¯}{t})$ over a field of characteristic p > 3, where $m,n\in \mathbb{N}+1$ and $\underset{¯}{t}=(t_1,t_2,\dots ,t_m)$ is an m-tuple of positive integers, and K has a finite $\mathbb{Z}$-graded structure. Let T_K be the canonical torus of K, which is an abelian subalgebra of K₀ and semisimple on $K_{-1}.$ Utilizing the weight space decomposition of K with respect to T_K, we prove in this paper that each skew-symmetric super-biderivation of K is inner.

Communicated by K. C. Misra

Keywords:

• Torus
• weight space decomposition
• super-biderivation

MATHEMATICS SUBJECT CLASSIFICATION (2010):

• 17B05
• 17B40
• 17B50

Acknowledgements

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

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.

Additional information

Funding

Supported by NNSF of China (Nos. 11771069), NSF of Jilin province (No. 20170101048JC) and the project of jilin province department of education (No. JJKH20180005K).