Lie bialgebras of generalized loop Virasoro algebras

TL;DR

This paper proves that all Lie bialgebra structures on generalized loop Virasoro algebras are coboundary triangular by showing the triviality of a specific cohomology group, and extends these results to generalized map Virasoro algebras.

Contribution

It establishes the triviality of the first cohomology group for generalized loop Virasoro algebras and characterizes their Lie bialgebra structures as coboundary triangular, extending to generalized map Virasoro algebras.

Findings

First cohomology group is trivial

Lie bialgebra structures are coboundary triangular

Results extended to generalized map Virasoro algebras

Abstract

The first cohomology group of a generalized loop Virasoro algebra with coefficients in the tensor product of its adjoint module is shown to be trivial. The result is applied to prove that Lie bialgebra structures on generalized loop Virasoro algebras are coboundary triangular. We then generalize the results to generalized map Virasoro algebras.