Non-formal deformation quantization of Fréchet-Poisson algebras: the Heisenberg and Lie algebra case

2007 ◽  
pp. 99-123 ◽  
Author(s):  
Hideki Omori ◽  
Yoshiaki Maeda ◽  
Naoya Miyazaki ◽  
Akira Yoshioka
Keyword(s):  
Lie Algebra ◽  
Deformation Quantization ◽  
Poisson Algebras ◽  
Formal Deformation

Non-Formal Deformation Quantization and Symmetric Spaces

2009 ◽  
Author(s):  
P. Bieliavsky ◽  
Piotr Kielanowski ◽  
S. Twareque Ali ◽  
Anatol Odzijewicz ◽  
Martin Schlichenmaier ◽  
...  
Keyword(s):  
Deformation Quantization ◽  
Symmetric Spaces ◽  
Formal Deformation

scholarly journals Quantization of a Poisson algebra and polynomials associated to links

1990 ◽  
Vol 120 ◽  
pp. 113-127 ◽  
Author(s):  
Tetsuya Ozawa
Keyword(s):  
Riemann Surface ◽  
Lie Algebra ◽  
Poisson Algebra ◽  
Homotopy Classes ◽  
Poisson Algebras

A formal quantization of Poisson algebras was discussed by several authors (see for instance Drinfel’d [D]). A formal Lie algebra generated by homotopy classes of loops on a Riemann surface ∑ was obtained by W. Goldman in [G], and its Poisson algebra was quantized, in the sense of Drinfel’d, by Turaev in [T].

scholarly journals W-algebras and Duflo isomorphism

2018 ◽  
Vol 17 (03) ◽  
pp. 1850041
Author(s):  
P. Batakidis ◽  
N. Papalexiou
Keyword(s):  
Lie Algebra ◽  
Deformation Quantization ◽  
Poisson Manifold ◽  
Product Formula ◽  
Poisson Structures ◽  
Semisimple Lie Algebra

We prove that when Kontsevich’s deformation quantization is applied on weight homogeneous Poisson structures, the operators in the ∗-product formula are weight homogeneous. In the linear Poisson case for a semisimple Lie algebra [Formula: see text] the Poisson manifold [Formula: see text] is [Formula: see text]. As an application we provide an isomorphism between the Cattaneo–Felder–Torossian reduction algebra [Formula: see text] and the [Formula: see text]-algebra [Formula: see text]. We also show that in the [Formula: see text]-algebra setting, [Formula: see text] is polynomial. Finally, we compute generators of [Formula: see text] as a deformation of [Formula: see text].

scholarly journals DEFORMATION QUANTIZATION OF CERTAIN NONLINEAR POISSON STRUCTURES

1998 ◽  
Vol 09 (05) ◽  
pp. 599-621 ◽  
Author(s):  
BYUNG-JAY KAHNG
Keyword(s):  
Poisson Bracket ◽  
Lie Algebra ◽  
Deformation Quantization ◽  
Dual Space ◽  
Poisson Brackets ◽  
Poisson Structures ◽  
Central Extensions ◽  
C Algebras ◽  
Lie Bracket ◽  
Compact Quantum Groups

As a generalization of the linear Poisson bracket on the dual space of a Lie algebra, we introduce certain nonlinear Poisson brackets which are "cocycle perturbations" of the linear Poisson bracket. We show that these special Poisson brackets are equivalent to Poisson brackets of central extension type, which resemble the central extensions of an ordinary Lie bracket via Lie algebra cocycles. We are able to formulate (strict) deformation quantizations of these Poisson brackets by means of twisted group C*-algebras. We also indicate that these deformation quantizations can be used to construct some specific non-compact quantum groups.

Deformation quantization of Fréchet-Poisson algebras: Convergence of the Moyal product

2000 ◽  
pp. 233-245 ◽  
Author(s):  
Hideki Omori ◽  
Yoshiaki Maeda ◽  
Naoya Miyazaki ◽  
Akira Yoshioka
Keyword(s):  
Deformation Quantization ◽  
Moyal Product ◽  
Poisson Algebras

scholarly journals Deformation quantization of Poisson algebras

1992 ◽  
Vol 68 (5) ◽  
pp. 97-100
Author(s):  
Hideki Omori ◽  
Yoshiaki Maeda ◽  
Akira Yoshioka
Keyword(s):  
Deformation Quantization ◽  
Poisson Algebras

Non-commutative Poisson Algebra Structures on the Lie Algebra $so_n\widetilde{({\Bbb C}_Q)}$

2007 ◽  
Vol 14 (03) ◽  
pp. 521-536 ◽  
Author(s):  
Jie Tong ◽  
Quanqin Jin
Keyword(s):  
Lie Algebra ◽  
Associative Algebra ◽  
Poisson Algebra ◽  
Algebra Structure ◽  
Poisson Algebras

Non-commutative Poisson algebras are the algebras having both an associative algebra structure and a Lie algebra structure together with the Leibniz law. In this paper, the non-commutative poisson algebra structures on [Formula: see text] are determined.

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