Brackets, superalgebras and spectral gap

  • Consuelo MartínezEmail author
  • Efim Zelmanov


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 \({\mathbb {C}}\).


Bracket Superalgebra Conformal algebra 

Mathematics Subject Classification

17B68 17B63 17C90 



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.

Author Contributions

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

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Instituto de Matemática e Estatística da Universidade de São Paulo 2019

Authors and Affiliations

  1. 1.Departmento de MatemáticasUniversidad de OviedoOviedoSpain
  2. 2.Department of MathematicsUniversity of California San DiegoLa JollaUSA

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