Comments:

December 1, 1998, 180 pages, freely downloadable as a 3.4MB PDF file, 21 Chapters, references and Index

Abstract:

This is a very useful book on non-commutative geometry and algebra, that can be downloaded as a 3.4 Mb PDF file. The authors describe `Noncommutative Geometry' as follows: \\"Noncommutative geometry is the study of noncommutative algebras as if they were algebras of functions on spaces, like the commutative algebras associated to affine algebraic varieties, differentiable manifolds, topological spaces, and measure spaces."\\ The following are the `highlights' from this `free' book (with authors' copyrights!): \\ "I Universal Enveloping Algebras 1 Algebraic Constructions. 1.1 Universal Enveloping Algebras. 1.2 Lie Algebra Deformations. 1.3 Symmetrization. 1.4 The Graded Algebra of U(g). \\\ 2 The Poincare'e-Birkhoff-Witt Theorem : II. Poisson Geometry. 3.3 Poisson Manifolds. 3.4 Structure Functions and Canonical Coordinates. 3.5 Hamiltonian Vector Fields . 3.6 Poisson Cohomology. \\\ 5 Local Poisson Geometry. 5.1 Symplectic Foliation. 5.2 Transverse Structure. 5.3 The Linearization Problem . 5.4 The Cases of su(2) and sl(2;R).\\ III Poisson Category. \\ Hamiltonian Actions 7.1. Momentum Maps. 7.2 First Obstruction for Momentum Maps . 7.3 Second Obstruction for Momentum Maps. 7.4 Killing the Second Obstruction. \\\ IV Dual Pairs, p.47, VIII. Operator Algebras. 8.1 Norm Topology and C*-Algebras. 8.2 Strong and Weak Topologies. 8.3 Commutants. 8.4 Dual Pairs. 9 Dual Pairs in Poisson Geometry. 9.1 Commutants in Poisson Geometry. 9.2 Pairs of Symplectically Complete Foliations. 9.3 Symplectic Dual Pairs. 9.4 Morita Equivalence. 10.4 The Harmonic Oscillator. 10.5 A Dual Pair from Complex Geometry. \\ V Generalized Functions. 11 Group Algebras. 11.1 Hopf Algebras. 11.2 Commutative and Noncommutative Hopf Algebras.\\ 11.3 Algebras of Measures on Groups.\\ 11.4 Convolution of Functions. \\ 11.5 Distribution Group Algebras. \\ 12 Densities. 12.1 Densities. 12.2 Intrinsic Lp Spaces. 12.3 Generalized Sections. \\\\ VI Groupoids p. 85. 13 Groupoids. \\ 14 Groupoid Algebras. 14.2 Groupoid Algebras via Haar Systems. 14.4 Groupoid Actions. 14.5 Groupoid Algebra Actions.\\ VII Algebroids, p.113. 16 Lie Algebroids, p. 113. 16.4 Integrability and Non-Integrability.\\ 16.5 The Dual of a Lie Algebroid . Differential Geometry for Lie Algebroids. p.131. 18.4 Poisson Cohomology on Lie Algebroids.\\ VIII Deformations of Algebras of Functions p.141. 19 Algebraic Deformation Theory p.141. 19.2 Hochschild Cohomology.\\ 20 Weyl Algebras p.149. 20.1 The Moyal-Weyl Product. The Moyal-Weyl Product as an Operator Product. Derivations of Formal Weyl Algebras. 20.5 Weyl Algebra Bundles, p.153. 21 Deformation Quantization p.155. 21.5 Classification of Deformation Quantizations, p.161. References, p.163. Index.

Rights:

Open access: authors copyright, free downloads http://www.math.ist.utl.pt/~acannas/Books/models_final.pdf

Links:

ISBN #:

No messages.