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Deformation Quantization technics for Lie Theory problems

 

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  • Product Description
 

In this book we''ll be using results and technics from deformation quantization of Poisson manifold theory in the sense Kontsevich and Cattaneo-Felder. The goal is to make suitable adaptations in order to use them in the Lie algebra case. This way we confront old problems of Lie theory and non commutative harmonic analysis. The first chapter is a detailed introduction to the part of the theory on (nilpotent) Lie groups and Lie algebras that we need. The second one is also a detailed introduction on deformation (bi)quantization and tools that we''ll use in the sequence. Towards the end of chapter 2 we explain how these results will be used to prove theorems in the Lie case and introduce some central objects of study. Chapter 3 contains a detailed proof of a non-canonical isomorphism between a well known algebra of invariant differential operators and the corresponding to these data reduction algebra from deformation quantization. In chapter 4 the question of equivalence between characters from deformation quantization and harmonic analysis on Lie groups is answered positively. Finally in chapter 5 a central worked out example provides an overview of the above put in action.

Product Specifications
SKU :COC42488
AuthorPanagiotis Batakidis
LanguageEnglish
BindingPaperback
Number of Pages212
Publishing Year2010-09-29T00:00:00.000
ISBN978-6131537127
Edition1 st
Book TypeAlgebra
Country of ManufactureIndia
Product BrandNot defined
Product Packaging InfoBox
In The Box1 Piece
Product First Available On ClickOnCare.com2015-01-08 00:00:00