Letters in Mathematical Physics

, Volume 108, Issue 10, pp 2293–2301 | Cite as

Nearly associative deformation quantization

  • Dmitri Vassilevich
  • Fernando Martins Costa Oliveira


We study several classes of non-associative algebras as possible candidates for deformation quantization in the direction of a Poisson bracket that does not satisfy Jacobi identities. We show that in fact alternative deformation quantization algebras require the Jacobi identities on the Poisson bracket and, under very general assumptions, are associative. At the same time, flexible deformation quantization algebras exist for any Poisson bracket.


Deformation quantization Nonassociative algebras Nongeometric string backgrounds 

Mathematics Subject Classification

81S99 17A20 



We are grateful to Ivan Shestakov, Vlad Kupriyanov and Richard Szabo for fruitful discussions. One of the authors (D.V.) was supported in part by the Grant 2016/03319-6 of the São Paulo Research Foundation (FAPESP), by the Grant 303807/2016-4 of CNPq, by the RFBR Project 18-02-00149-a, and by the Tomsk State University Competitiveness Improvement Program. The other author (F.M.C.O.) was supported by CAPES.


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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.CMCCUniversidade Federal do ABCSanto AndréBrazil
  2. 2.Department of PhysicsTomsk State UniversityTomskRussia

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