2-local derivations on the twisted Heisenberg-Virasoro algebra

Zhao, Yufang; Cheng, Yongsheng

doi:10.48550/arxiv.2103.04228

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2024

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“…The derivation algebra and automorphism group on the twisted Heisenberg-Virasoro algebra have been determined (see [12]). Two-local derivations on the twisted Heisenberg-Virasoro algebra are also given in [13]. The mirror Heisenberg-Virasoro algebra is defined as 1 2 Z-graded algebra, and its 1 2 Z-graded derivation algebras are given in [14].…”

Section: Introductionmentioning

confidence: 99%

Maps on the Mirror Heisenberg–Virasoro Algebra

Guo,

Kaygorodov,

Tang

2024

Mathematics

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Using the first cohomology from the mirror Heisenberg–Virasoro algebra to the twisted Heisenberg algebra (as the mirror Heisenberg–Virasoro algebra module), in this paper, we determined the derivations on the mirror Heisenberg–Virasoro algebra. Based on this result, we proved that any two-local derivation on the mirror Heisenberg–Virasoro algebra is a derivation. All half-derivations are described, and as corollaries, we have descriptions of transposed Poisson structures and local (two-local) half-derivations on the mirror Heisenberg–Virasoro algebra.

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