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Geometric Models

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Geometric Models for
Noncommutative Algebras
Ana Cannas da Silva,
Alan Weinstein

Table of Contents

I Universal Enveloping Algebras

1 Algebraic Constructions

2 The Poincar ́-Birkhoff-Witt Theorem

II Poisson Geometry

3 Poisson Structures

4 Normal Forms

5 Local Poisson Geometry

III Poisson Category

6 Poisson Maps

7 Hamiltonian Actions

IV Dual Pairs

8 Operator Algebras

9 Dual Pairs in Poisson Geometry

10 Examples of Symplectic Realizations

V Generalized Functions

11 Group Algebras

12 Densities

VI Groupoids

13 Groupoids

14 Groupoid Algebras

15 Extended Groupoid Algebras

VII Algebroids

16 Lie Algebroids

17 Examples of Lie Algebroids

18 Differential Geometry for Lie Algebroids

VIII Deformations of Algebras of Functions

19 Algebraic Deformation Theory

20 Weyl Algebras

21 Deformation Quantization

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