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ℤ2-GRADED POISSON ALGEBRAS, THEIR DEFORMATIONS AND COHOMOLOGY IN LOW DIMENSIONS

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Abstract

We study ℤ2-graded Poisson structures defined on ℤ2-graded commutative polynomial algebras. In small-dimensional cases, we obtain the associated Poisson ℤ2-graded cohomology and in some cases, deformations of these Poisson brackets and P∞-algebra structures. We highlight differences and analogies between this ℤ2-graded context and the non-graded context, by studying, for example, the links between Poisson cohomology and singularities.

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Authors and Affiliations

  1. University of Wisconsin, Eau Claire, WI, 54702-4004, USA

    M. PENKAVA

  2. Université de Lyon, Institut Camille Jordan (UMR 5208), Université de Saint-Etienne, Faculté des Sciences, 23, Rue Docteur Paul Michelon, 42023, Saint-Etienne Cedex 2, France

    A. PICHEREAU

Authors
  1. M. PENKAVA
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  2. A. PICHEREAU
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Correspondence to A. PICHEREAU.

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PENKAVA, M., PICHEREAU, A. ℤ2-GRADED POISSON ALGEBRAS, THEIR DEFORMATIONS AND COHOMOLOGY IN LOW DIMENSIONS. Transformation Groups 23, 1091–1127 (2018). https://doi.org/10.1007/s00031-017-9465-2

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