Geometric Models for Noncommutative Algebra by Ana Cannas da Silva, Alan Weinstein - Free PDF
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About this book :-
This book explains how certain algebraic structures called noncommutative algebras can be understood as if they were collections of functions on geometric spaces.
This text begins with basic concepts and gradually progresses to more advanced topics. Central to the discussion are symplectic and Poisson manifolds, which are geometric structures that arise when noncommutative algebras are obtained by deforming commutative algebras. The authors also give a detailed study of groupoids and Lie algebroids, which serve as infinitesimal approximations to differentiable groupoids.
In this work, the authors discuss several types of geometric objects that are closely related to noncommutative algebras. Central to the discussion are symplectic and Poisson manifolds, which arise when noncommutative algebras are obtained by deforming commutative algebras. Noncommutative geometry is the study of noncommutative algebras as if they were algebras of functions on spaces, for example, the commutative algebras associated to affine algebraic varieties, differentiable manifolds, topological spaces, and measure spaces.
Book Detail :-
This book has following details information.
Title:
Geometric Models for Noncommutative Algebra by Ana Cannas da Silva, Alan Weinstein - Free PDF
Publisher:
University of California at Berkeley
Year:
1998
Pages:
194
Type:
PDF
Language:
English
ISBN-10 #:
0821809520
ISBN-13 #:
978-0821809525
License:
N\A
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About Author :-
The author NA
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Book Contents :-
This book has following table of contents.
Part-I Universal Enveloping Algebras
1. Algebraic Constructions
2. The Poincar´e-Birkhoff-Witt Theorem
Part-II Poisson Geometry
3. Poisson Structures
4. Normal Forms
5. Local Poisson Geometry
Part-III Poisson Category
6. Poisson Maps
7. Hamiltonian Actions
Part-IV Dual Pairs
8. Operator Algebras
9. Dual Pairs in Poisson Geometry
10. Examples of Symplectic Realizations
Part-V Generalized Functions
11. Group Algebras
12. Densities
Part-VI Groupoids
13. Groupoids
14. Groupoid Algebras
15. Extended Groupoid Algebras
Part-VII Algebroids
16. Lie Algebroids
17. Examples of Lie Algebroids
18. Differential Geometry for Lie Algebroids
Part-VIII Deformations of Algebras of Functions
19. Algebraic Deformation Theory
20. Weyl Algebras
21. Deformation Quantization
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