Lie super-bialgebra structures on the Lie superalgebra of Witt type

Abstract

In this article, Lie super-bialgebra structures on the Lie superalgebra of Witt type $\mathcal{W}$ are investigated. They are shown to be triangular coboundary. As a byproduct, we obtain that the first cohomology group $H^1(\mathcal{W},\mathcal{W}\otimes \mathcal{W})$ is trivial.

Keywords:

• Lie superalgebras of Witt type
• Lie super-bialgebras
• Yang-Baxter equation

MATHEMATICS SUBJECT CLASSIFICATION (2000):

• 17B62
• 17B05
• 17B37
• 17B66

Acknowledgments

We wish to thank the referee for the advice to make the paper more readable, and to make the proof of Claim 2 in Proposition 4.1 more clear.

Additional information

Funding

This article was supported by NSF [Grant Nos. 11431010 and 11971350] of China.