Ben Amar, Nabiha and Chaabouni, Mouna and Hfaiedh, Mabrouka:
Kontsevich Deformation Quantization on Lie Algebras
Bollettino dell'Unione Matematica Italiana Serie 8 10-B (2007), fasc. n.2, p. 365-379, Unione Matematica Italiana (English)
pdf (461 Kb), djvu (145 Kb). | MR 2339447 | Zbl 1178.53092
Sunto
Consideriamo il prodotto star di Kontsevich sul duale $\frak{g}^*$ di una algebra di Lie generale g dotata di parentesi di Poisson lineare. Mostriamo che questo prodotto star fornisce una quantizzazione di deformazione mediante immersioni parziali nella direzione della parentesi di Poisson.
Referenze Bibliografiche
[AB]
D. ARNAL -
N. BEN AMAR,
Kontsevich's Wheels and Invariant Polynomial Functions on the Dual of Lie Algebras,
Lett. Math. Phys.,
52 (
2000), 291-300. |
fulltext (doi) |
MR 1796573 |
Zbl 1017.53073[B]1
N. BEN AMAR,
Tangential Deformations on the Dual of Nilpotent Special Lie Algebras,
Pacific Journal of Mathematics,
170, no. 2 (
1995), 297-318. |
MR 1363867 |
Zbl 0847.17018[B]3
N. BEN AMAR,
A Comparison between Rieffel's and Kontsevich's Deformation Quantizations for Linear Poisson Tensors, To appear in
Pacific Journal of Mathematics. |
fulltext (doi) |
MR 2276500 |
Zbl 1155.53337[BFFLS]
F. BAYEN -
M. FLATO -
C. FRONSDAL -
A. LICHNEROWICZ -
D. STERNHEIMER,
Deformation Theory and Quantization, I, II,
Ann. of Phys.,
111 (
1978), 61-151. |
fulltext (doi) |
MR 496157 |
Zbl 0377.53025[DL]
M. DE WILDE -
P. LECOMTE,
Existence of Star Products and of Formal Deformations of the Poisson Lie Algebras of Arbitary Symplectic Manifold,
Lett. Math. Phys.,
7 (
1983), 487-496. |
fulltext (doi) |
MR 728644 |
Zbl 0526.58023[F]
B. F. FEDESOV,
A Simple Geometrical Construction of Deformation Quantization,
J.D.G,
40 (
1994), 213-238. |
MR 1293654[K] M. KONTSEVICH, Deformation Quantization of Poisson Manifolds, I. q-alg/9709040 (1997).
[OMY]
H. OMORI -
Y. MAEDA -
A. YOSHIOKA,
Weyl Manifolds and Deformation Quantization,
Adv. in Math.,
85 (
1991), 225-255. |
fulltext (doi) |
MR 1093007[P]
G. K. PEDERSEN,
$C^*$-Algebras and their Automorphism Groups,
London Math. Soc. Monographs,
14,
Academic Press, London, (
1979). |
MR 548006[R]1
M. A. RIEFFEL Lie Group Convolution Algebras as Deformation Quantizations of Linear Poisson Structures,
Amer. J. Math.,
112 (
1990), 657-686. |
fulltext (doi) |
MR 1064995 |
Zbl 0713.58054[R]2
M. A. RIEFFEL,
Deformation Quantization of Heisenberg Manifolds,
Comm. Math. Phys.,
122 (
1989), 531-562. |
MR 1002830 |
Zbl 0679.46055[V]
V.S. VARADARAJAN,
Lie Groups, Lie Algebras and their Representations Prentice-Hall, New Jersey (
1974). |
MR 376938 |
Zbl 0371.22001[W]
A. WEINSTEIN,
The Local Structure of Poisson Manifolds,
J. Diff. Geom.,
18 (
1983) 523-557. |
MR 723816 |
Zbl 0524.58011