The characteristic classes of Morita equivalent star products on symplectic manifolds

被引：31

作者：

Bursztyn, H ^{[1
]}

Waldmann, S

机构：

[1] Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 USA

[2] Univ Freiburg, Fak Phys, D-79104 Freiburg, Germany

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2002年 / 228卷 / 01期

关键词：

D O I：

10.1007/s002200200657

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

In this paper we give a complete characterization of Morita equivalent star products on symplectic manifolds in terms of their characteristic classes: two star products star and star' on (M,omega) are Morita equivalent if and only if there exists a symplectomorphism psi : M --> M such that the relative class t(star, psi*(star')) is 2pi i-integral. For star products on cotangent bundles, we show that this integrality condition is related to Dirac's quantization condition for magnetic charges.

引用

页码：103 / 121

页数：19

共 37 条

[11] Semiclassical geometry of quantum line bundles and Morita equivalence of star products [J].

Bursztyn, H .

INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2002, 2002 (16) :821-846

[12] Algebraic Rieffel induction, formal Morita equivalence, and applications to deformation quantization [J].

Bursztyn, H ;

Waldmann, S .

JOURNAL OF GEOMETRY AND PHYSICS, 2001, 37 (04) :307-364

[13] *-Ideals and formal Morita equivalence of *-algebras [J].

Bursztyn, H ;

Waldmann, S .

INTERNATIONAL JOURNAL OF MATHEMATICS, 2001, 12 (05) :555-577

[14] Deformation quantization of Hermitian vector bundles [J].

Bursztyn, H ;

Waldmann, S .

LETTERS IN MATHEMATICAL PHYSICS, 2000, 53 (04) :349-365

[15]

Connes A, 1998, J HIGH ENERGY PHYS

[16] EXISTENCE OF STAR-PRODUCTS AND OF FORMAL DEFORMATIONS OF THE POISSON LIE-ALGEBRA OF ARBITRARY SYMPLECTIC-MANIFOLDS [J].

DEWILDE, M ;

LECOMTE, PBA .

LETTERS IN MATHEMATICAL PHYSICS, 1983, 7 (06) :487-496

[17] A SIMPLE GEOMETRICAL CONSTRUCTION OF DEFORMATION QUANTIZATION [J].

FEDOSOV, BV .

JOURNAL OF DIFFERENTIAL GEOMETRY, 1994, 40 (02) :213-238

[18] ON DEFORMATION OF RINGS + ALGEBRAS [J].

GERSTENHABER, M .

ANNALS OF MATHEMATICS, 1964, 79 (01) :59-&

[19]

Gutt S, 2000, MATH PHYS S, V21, P217

[20] Equivalence of star products on a symplectic manifold;: an introduction to Deligne's Cech cohomology classes [J].

Gutt, S ;

Rawnsley, J .

JOURNAL OF GEOMETRY AND PHYSICS, 1999, 29 (04) :347-392

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