Maps on the Mirror Heisenberg–Virasoro Algebra

Xuelian Guo, Ivan Kaygorodov and Liming Tang ()
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Xuelian Guo: School of Mathematical Sciences, Harbin Normal University, Harbin 150025, China
Ivan Kaygorodov: CMA-UBI, Universidade da Beira Interior, 6201-001 Covilhã, Portugal
Liming Tang: School of Mathematical Sciences, Harbin Normal University, Harbin 150025, China

Mathematics, 2024, vol. 12, issue 6, 1-17

Abstract: 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.

Keywords: derivation; two-local derivation; half-derivation; Lie algebra (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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