Lie Bialgebras on the Rank Two Heisenberg–Virasoro Algebra

Yihong Su and Xue Chen ()
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Yihong Su: School of Mathematics and Statistics, Xiamen University of Technology, Xiamen 361024, China
Xue Chen: School of Mathematics and Statistics, Xiamen University of Technology, Xiamen 361024, China

Mathematics, 2023, vol. 11, issue 4, 1-17

Abstract: 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.

Keywords: the rank two Heisenberg–Virasoro algebra; Lie bialgebras; Yang–Baxter equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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