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Brackets, superalgebras and spectral gap

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Abstract

The purpose of this survey is to discuss Poisson and contact brackets and related infinite dimensional superalgebras. All vector spaces are considered over the field of complex numbers \({\mathbb {C}}\).

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Acknowledgements

The first author has been partially supported by the Projects MTM 2017-83506-C2-2-P from the Ministry of Economy of Spain and FC-GRUPIN-IDI/2018/000193 from the Principado de Asturias, the second author gratefully acknowledges the support by the NSF Grant DMS 160 1920.

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Authors and Affiliations

  1. Departmento de Matemáticas, Universidad de Oviedo, C/Calvo Sotelo, s/n, 33007, Oviedo, Spain

    Consuelo Martínez

  2. Department of Mathematics, University of California San Diego, 9500 Gilman Drive, La Jolla, CA, 92093-0112, USA

    Efim Zelmanov

Authors
  1. Consuelo Martínez
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  2. Efim Zelmanov
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Contributions

CM, EZ designed research, performed research, and wrote the paper.

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Correspondence to Consuelo Martínez.

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The authors declare that they have no conflict of interest.

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To our friend and colleague Ivan Shestakov with respect and affection..

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The survey is based on our forthcoming paper with O. Mathieu. The authors thank him for useful discussions during the preparation of the survey.

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Martínez, C., Zelmanov, E. Brackets, superalgebras and spectral gap. São Paulo J. Math. Sci. 13, 112–132 (2019). https://doi.org/10.1007/s40863-019-00128-5

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