Lie bialgebra structures on the deformative Schrödinger-Virasoro algebras

The rank two Heisenberg–Virasoro algebra can be viewed as a generalization of the twisted Heisenberg–Virasoro algebra. Lie bialgebras play an important role in searching for solutions of quantum Yang–Baxter equations. It is interesting to study the Lie bialgebra structures on the rank two Heisenberg–Virasoro algebra. Since the Lie brackets of rank two Heisenberg–Virasoro algebra are different from that of the twisted Heisenberg–Virasoro algebra and Virasoro-like algebras, and there are inner derivations (from itself to its tensor space) which are hidden more deeply in its interior algebraic structure, some new techniques and strategies are employed in this paper. It is proved that every Lie bialgebra structure on the rank two Heisenberg–Virasoro algebra is triangular coboundary.

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Lie Bialgebra Structures on the Lie Algebra L Related to the Virasoro Algebra

Chen

Zheng

2023

Symmetry

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A Lie bialgebra is a vector space endowed simultaneously with the structure of a Lie algebra and the structure of a Lie coalgebra, and some compatibility condition. Moreover, Lie brackets have skew symmetry. Because of the close relation between Lie bialgebras and quantum groups, it is interesting to consider the Lie bialgebra structures on the Lie algebra L related to the Virasoro algebra. In this paper, the Lie bialgebras on L are investigated by computing Der(L, L⊗L). It is proved that all such Lie bialgebras are triangular coboundary, and the first cohomology group H1(L, L⊗L) is trivial.

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Lie bialgebra structures on the deformative Schrödinger-Virasoro algebras

Abstract: In this paper we investigate Lie bialgebra structures on the deformative Schrödinger-Virasoro algebras mainly using the techniques introduced recently by Liu, Pei and Zhu, which indicate that all cases considered in this paper except one behave different from their centerless ones.

Cited by 3 publications

References 38 publications

Lie bialgebra structures on generalized loop Schrödinger-Virasoro algebras

Lie bialgebra structures on generalized loop Schrödinger-Virasoro algebras

Lie Bialgebras on the Rank Two Heisenberg–Virasoro Algebra

Lie Bialgebra Structures on the Lie Algebra L Related to the Virasoro Algebra

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