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Note on Poisson cohomology on Weil bundles

Volume 122 / 2019

Basile Guy Richard Bossoto, Olivier Mabiala Mikanou, Apépé Jugendène Nguéngué Louvouandou Annales Polonici Mathematici 122 (2019), 1-9 MSC: Primary 53D17; Secondary 58A20. DOI: 10.4064/ap180207-22-10 Published online: 8 February 2019

Abstract

The purpose of this note on Poisson cohomology is to show that if $M$ is a Poisson manifold and if $A$ is a Weil algebra, then the Weil bundle $M^{A}$ is a Poisson manifold. Therefore, we establish a relationship between Poisson cohomology $H_{\{\cdot ,\cdot \}_{A}}^{\bullet }(M^{A},A)$ with values in $A$ and Poisson cohomology $H_{\{\cdot ,\cdot \},\mathbb {R}}^{\bullet }(M^{A})$ with real values.

Authors

  • Basile Guy Richard BossotoDepartment of Mathematics
    Faculty of Sciences and Technology
    Marien Ngouabi University
    and
    Institut de Recherche
    en Sciences Exactes et Naturelles (IRSEN)
    Box 69
    Brazzaville, Congo
    e-mail
  • Olivier Mabiala MikanouDepartment of Mathematics
    Faculty of Sciences and Technology
    Marien Ngouabi University
    Box 69
    Brazzaville, Congo
    e-mail
  • Apépé Jugendène Nguéngué LouvouandouDepartment of Mathematics
    Faculty of Sciences and Technology
    Marien Ngouabi University
    Box 69
    Brazzaville, Congo
    e-mail

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