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Maps on the Mirror Heisenberg–Virasoro Algebra

Author

Listed:
  • Xuelian Guo

    (School of Mathematical Sciences, Harbin Normal University, Harbin 150025, China)

  • Ivan Kaygorodov

    (CMA-UBI, Universidade da Beira Interior, 6201-001 Covilhã, Portugal
    Saint Petersburg University, 199034 St. Petersburg, Russia)

  • Liming Tang

    (School of Mathematical Sciences, Harbin Normal University, Harbin 150025, China)

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.

Suggested Citation

  • Xuelian Guo & Ivan Kaygorodov & Liming Tang, 2024. "Maps on the Mirror Heisenberg–Virasoro Algebra," Mathematics, MDPI, vol. 12(6), pages 1-17, March.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:6:p:802-:d:1353876
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