# Lie superbialgebra structures on the twisted N=1 Schr\"{o}dinger-Neveu-Schwarz algebra

## TL;DR

This paper classifies Lie superbialgebra structures on the twisted N=1 Schrödinger-Neveu-Schwarz algebra, providing conditions for coboundary triangular structures and computing its first cohomology group.

## Contribution

It offers a complete description of superbialgebra structures on the algebra and determines the first cohomology group with specific coefficients, advancing understanding of its algebraic properties.

## Key findings

- Characterization of superbialgebra structures on the algebra
- Necessary and sufficient conditions for coboundary triangular structures
- Complete determination of the first cohomology group

## Abstract

Lie superbialgebra structures on the twisted N=1 Schr\"{o}dinger-Neveu-Schwarz algebra $\frak{tsns}$ are described. The corresponding necessary and sufficient conditions for such superbialgebra to be coboundary triangular are given. Meanwhile, the first cohomology group of $\frak{tsns}$ with coefficients in the tensor product of its adjoint module is completely determined.