Lie super-bialgebra structures on a class of generalized super W-algebra L

Abstract

In this paper, Lie super-bialgebra structures on a class of generalized super W-algebra $\mathfrak{L}$ are investigated. By proving the first cohomology group of $\mathfrak{L}$ with coefficients in its adjoint tensor module is trivial, namely, $H^1(\mathfrak{L},\mathfrak{L}\otimes \mathfrak{L})=0$, we obtain that all Lie super-bialgebra structures on $\mathfrak{L}$ are triangular coboundary.

Keywords:

• Cohomology group
• generalized super W-algebras
• Lie super-bialgebra

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 17B05
• 17B62
• 17B65
• 17B68

Additional information

Funding

This work is supported by the Fundamental Research Funds for the Central Universities, No. JZ2018HGBZ0123, NSF grants 11701047, 11671056, and a NSF grant BK20160403 of Jiangsu Province.