Super-biderivations of the generalized Witt Lie superalgebra W(m,n;t)

Abstract

Let W denote the generalized Witt Lie superalgebra $W(m,n;\underset{\_}{t})$ over a field of characteristic p>2. Utilizing the abelian subalgebra T and the weight space decomposition of W with respect to T, we show the action of the skew-symmetric super-biderivation on the elements of T and the generators of W. Moreover, we prove that each skew-symmetric super-biderivation of W is inner.

COMMUNICATED BY:

• Mikhail Chebotar

Keywords:

• Torus
• weight space decomposition
• biderivations

Mathematics Subject Classification (2010):

• 17B05
• 17B40
• 17B50

Acknowledgments

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

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Supported by NNSF of China (Nos. 11771069, 11801121), NSF of Jilin province (No. 20170101048JC), the project of Jilin province department of education (No. JJKH20180005K), NSF of Heilongjiang province (No. QC2018006), and the Fundamental Research Foundation for Universities of Heilongjiang Province (No. LGYC2018JC002).