Transposed Poisson Algebra Structures on Generalized Heisenberg–Virasoro Algebra of Rank Two

Abstract

In this paper, we describe transposed Poisson algebra structures on the Heisenberg–Virasoro algebra L of rank two and its generalization L(p, q), where p, q ∈ ℂ. We show that transposed Poisson algebra structures are trivial on L as well as on L(p, q) when (p, q) ∉ ℤ × ℤ. We then describe all nontrivial transposed Poisson algebra structures on L(p, q) for (p, q) ∈ ℤ × ℤ. Specifically, we classify the nontrivial transposed Poisson algebra structures on L(0, 0).

Keywords

Block Lie algebra / transposed Poisson algebra structure / ${1 \over 2}$-derivation')">${1 \over 2}$-derivation / 17B05 / 17B40 / 17B68

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Peking University