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Deformation Quantization technics for Lie Theory problems: An application of Kontsevich's deformation quantization technics to solve problems on invariant differential operators on Lie groups - Couverture souple

Batakidis, Panagiotis

 
9786131537127: Deformation Quantization technics for Lie Theory problems: An application of Kontsevich's deformation quantization technics to solve problems on invariant differential operators on Lie groups
Couverture souple
ISBN 10 : 6131537127 ISBN 13 : 9786131537127
Editeur : Editions universitaires europeennes, 2010

Synopsis

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.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

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.

Biographie de l'auteur

Panagiotis Batakidis, Doctorat in Mathematics from Universite? Denis Diderot,Paris. Previously he has been a researcher at the EU's RTN LIEGRITS, visiting researcher at the University of Antwerp and the Free University of Brussels. Currently (Septembre 2010) he is a visiting researcher at the Aristotle University of Thessaloniki.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
Editions universitaires europeennes
Date d'édition
2010
Langue
anglais
ISBN 10 
6131537127
ISBN 13 
9786131537127
Reliure
Broché
Nombre de pages
212
Coordonnées du fabricant
non disponible
Personne responsable
non disponible