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Letters in Mathematical Physics

, Volume 41, Issue 2, pp 101–117 | Cite as

Noncommutative Deformation Theory

  • Georges Pinczon
Article

Abstract

In Gerstenhaber's classical theory of deformations, the deformation parameter commutes with the original algebra. Motivated by some non classical deformations which recently appeared for quantization of Nambu mechanics, we introduce new deformations where the parameter no longer commutes with the original algebra. We find the associated cohomology and Gerstenhaber algebra and give rigidity and integrability criterions. We show that the Weyl algebra (though rigid in classical theory) can be nontrivially deformed, in super-commutative theory, to the supersymmetry enveloping algebra \(\mathcal{U}\;\left( {{\text{osp}}\left( {{\text{1,2}}} \right)} \right)\)

deformations cohomology quantization Gerstenhaber algebra. 

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Copyright information

© Kluwer Academic Publishers 1997

Authors and Affiliations

  • Georges Pinczon
    • 1
  1. 1.Laboratoire de Physique-MathematiqueUniversité de BourgogneDijonFrance

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