Lie bialgebras of generalized loop 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.

Quantization of the Super-BMS3 Algebra

“…Since then, the study of quantizations of Lie (super-)bialgebras has attracted more and more attention. A growing number of people studied the structure theory of Lie (super-)bialgebras, such as [6][7][8][9][10][11].…”

Lie Super-Bialgebras on Generalized Loop Super-Virasoro Algebras

“…A Lie bialgebra is a semiclassical structure of some quantum group. In recent decades, some articles about Lie bialgebras (superbialgebra) appeared (e.g., [2,3,12,13,16,18]). In [13], Lie bialgebra structures on the one-sided Witt algebra, the Witt algebra, and the Virasoro algebra are completely classified, which are shown to be triangular coboundary.…”

Structures of Not-finitely Graded Lie Superalgebras

“…The theory of Lie superalgebras plays a prominent role in modern mathematics and physics. In recent years, structures of all kinds of Lie superalgebras have aroused many scholars' great interests [1][2][3][4]. In this paper, we shall investigate the structure theory of a class of not-finitely graded Lie superalgebras related to the generalized super-Virasoro algebras (namely, derivations, automorphisms, 2-cocycles).…”

“…It plays a very important role in mathematics and physics. The structure and representation theories of (generalized) super-Virasoro algebra have been extensively undertaken by many authors [1,3,[11][12][13][14][15][16][17]. The generalized super-Virasoro algebra SVir[Γ, s] is a Lie superalgebra whose even part 0 SV has a basis {L α , C|α∈Γ} and odd part 1 SV has a basis {G µ |µ∈Γ+s}, equipped with the following Lie superbrackets: In the present work, we will consider the following Lie superalgebra, called not-finitely graded generalized super-Virasoro algebra [Γ, s], which has a basis {L α,i , G µ,j ||α∈Γ,µ∈s+Γ,i, j∈+}, and satisfies the following relations:…”