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Deformation Quantization of Polynomial Poisson Algebras

Identifieur interne : 001446 ( Main/Exploration ); précédent : 001445; suivant : 001447

Deformation Quantization of Polynomial Poisson Algebras

Auteurs : Michael Penkava ; Pol Vanhaecke [France]

Source :

Journal of Algebra [ 0021-8693 ] ; 2000.

RBID : ISTEX:2874E19BF29780393808D55F15BC036518B9BDD1

English descriptors

KwdEn :
- Algebra, Algebra homomorphism, Associative, Associative algebra, Associativity, Balanced deformation, Basis elements, Biderivation, Bracket, Cayley graph, Coboundary, Cycl, Deformation, Deformation quantization, Derivative, Diamond relation, Diamond relations, Explicit formula, Formal deformation quantization, Fourth order deformation, Fourth order term, Hand side, Hochschild coboundary operator, Injective, Injectivity, Jacobi, Jacobi identity, Matrix, Obstruction, Order deformation, Penkava, Poisson, Poisson algebra, Poisson algebras, Poisson bracket, Poisson matrix, Polynomial algebra, Polynomial poisson algebra, Quadratic bracket, Quantization, Quantized, Symmetric algebra, Symmetric cochain, Third order deformation, Third order term, Tridifferential operator, Vanhaecke, Vector space, deformation quantization, universal enveloping algebras.
Teeft :
- Algebra, Algebra homomorphism, Associative, Associative algebra, Associativity, Balanced deformation, Basis elements, Biderivation, Bracket, Cayley graph, Coboundary, Cycl, Deformation, Deformation quantization, Derivative, Diamond relation, Diamond relations, Explicit formula, Formal deformation quantization, Fourth order deformation, Fourth order term, Hand side, Hochschild coboundary operator, Injective, Injectivity, Jacobi, Jacobi identity, Matrix, Obstruction, Order deformation, Penkava, Poisson, Poisson algebra, Poisson algebras, Poisson bracket, Poisson matrix, Polynomial algebra, Polynomial poisson algebra, Quadratic bracket, Quantization, Quantized, Symmetric algebra, Symmetric cochain, Third order deformation, Third order term, Tridifferential operator, Vanhaecke, Vector space.

Abstract

Abstract: This paper discusses the notion of a deformation quantization for an arbitrary polynomial Poisson algebra A. We compute an explicit third order deformation quantization of A and show that it comes from a quantized enveloping algebra. We show that this deformation extends to a fourth order deformation if and only if the quantized enveloping algebra gives a fourth order deformation; moreover we give an example where the deformation does not extend. A correction term to the third order quantization given by the enveloping algebra is computed, which precisely cancels the obstruction, so that the modified third order deformation extends to a fourth order one. The solution is generically unique, up to equivalence.

Url:

https://api.istex.fr/document/2874E19BF29780393808D55F15BC036518B9BDD1/fulltext/pdf

DOI: 10.1006/jabr.1999.8239

Affiliations:

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Le document en format XML

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Deformation Quantization of Polynomial Poisson Algebras

Deformation Quantization of Polynomial Poisson Algebras

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English descriptors

Abstract

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