Letters in Mathematical Physics

, Volume 109, Issue 3, pp 623–641 | Cite as

A simple construction of associative deformations

  • Alexey A. SharapovEmail author
  • Evgeny D. Skvortsov


We propose a simple approach to formal deformations of associative algebras. It exploits the machinery of multiplicative coresolutions of an associative algebra A in the category of A-bimodules. Specifically, we show that certain first-order deformations of A extend to all orders and we derive explicit recurrent formulas determining this extension. In physical terms, this may be regarded as the deformation quantization of noncommutative Poisson structures on A.


Deformation quantization Noncommutative Poisson structures Symplectic reflection algebras Injective resolution 

Mathematics Subject Classification

Primary 16S80 Secondary 16E40 53D55 



We are grateful to Xiang Tang for a useful correspondence. We also thank the anonymous referee for many valuable remarks.


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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Physics FacultyTomsk State UniversityTomskRussia
  2. 2.Albert Einstein InstitutePotsdam-GolmGermany
  3. 3.Lebedev Institute of PhysicsMoscowRussia

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