Ali Baklouti – författare

Representation Theory and C*-algebras is devoted to the representation theory of solvable Lie groups and the associated non-commutative harmonic analysis including the study of C*-algebras. It contains full proofs of long-standing problems in the theory, including several polynomial conjectures and primitive zero ideals descriptions. It provides an in-depth study of their structural properties, the classification of unitary representations using the orbit method, and the underlying algebraic and analytic frameworks.

The book is most suitable for doctoral students, postdoctoral fellows, and researchers specializing in Lie theory, noncommutative geometry, functional analysis, operator algebras, and theoretical physics.

Features

· Complete solutions to polynomial conjectures (Corwin–Greenleaf and Duflo) in both nilpotent and exponential Lie group settings

· Complete results to long-standing problems about intertwining operators and the structure of primitive ideals in the exponential setting

· Comprehensive analysis of Casimir elements based on a new approach and their role in several related problems

· Detailed study of C*-algebras of solvable Lie groups, via methods using the Fourier transform and the spectral analysis

· Rich examples and counterexamples, including Heisenberg, thread-like, and G6 groups

· Bridge between classical and modern methods in representation theory, with applications to harmonic analysis and mathematical physics

Representation Theory and C*-algebras is devoted to the representation theory of solvable Lie groups and the associated non-commutative harmonic analysis including the study of C*-algebras. It contains full proofs of long-standing problems in the theory, including several polynomial conjectures and primitive zero ideals descriptions. It provides an in-depth study of their structural properties, the classification of unitary representations using the orbit method, and the underlying algebraic and analytic frameworks.

The book is most suitable for doctoral students, postdoctoral fellows, and researchers specializing in Lie theory, noncommutative geometry, functional analysis, operator algebras, and theoretical physics.

Features

· Complete solutions to polynomial conjectures (Corwin–Greenleaf and Duflo) in both nilpotent and exponential Lie group settings

· Complete results to long-standing problems about intertwining operators and the structure of primitive ideals in the exponential setting

· Comprehensive analysis of Casimir elements based on a new approach and their role in several related problems

· Detailed study of C*-algebras of solvable Lie groups, via methods using the Fourier transform and the spectral analysis

· Rich examples and counterexamples, including Heisenberg, thread-like, and G6 groups

· Bridge between classical and modern methods in representation theory, with applications to harmonic analysis and mathematical physics

This book presents a number of important contributions focusing on harmonic analysis and representation theory of Lie groups. All were originally presented at the 5th Tunisian–Japanese conference “Geometric and Harmonic Analysis on Homogeneous Spaces and Applications”, which was held at Mahdia in Tunisia from 17 to 21 December 2017 and was dedicated to the memory of the brilliant Tunisian mathematician Majdi Ben Halima. The peer-reviewed contributions selected for publication have been modified and are, without exception, of a standard equivalent to that in leading mathematical periodicals. Highlighting the close links between group representation theory and harmonic analysis on homogeneous spaces and numerous mathematical areas, such as number theory, algebraic geometry, differential geometry, operator algebra, partial differential equations and mathematical physics, the book is intended for researchers and students working in the area of commutative and non-commutative harmonic analysis as well as group representations.

This book collects a series of important works on noncommutative harmonic analysis on homogeneous spaces and related topics. All the authors participated in the 6th Tunisian-Japanese conference "Geometric and Harmonic Analysis on homogeneous spaces and Applications" held at Djerba Island in Tunisia during the period of December 16-19, 2019. The aim of this conference and the five preceding Tunisian-Japanese meetings was to keep up with the active development of representation theory interrelated with various other mathematical fields, such as number theory, algebraic geometry, differential geometry, operator algebra, partial differential equations, and mathematical physics. The present volume is dedicated to the memory of Takaaki Nomura, who organized the series of Tunisian-Japanese conferences with great effort and enthusiasm. The book is a valuable resource for researchers and students working in various areas of analysis, geometry, and algebra in connection with representation theory.

This book contains the latest developments of the theory of discontinuous groups acting on homogenous spaces, from basic concepts to a comprehensive exposition. It develops the newest approaches and methods in the deformation theory of topological modules and unitary representations and focuses on the geometry of discontinuous groups of solvable Lie groups and their compact extensions. It also presents proofs of recent results, computes fundamental examples, and serves as an introduction and reference for students and experienced researchers in Lie theory, discontinuous groups, and deformation (and moduli) spaces.

This book includes selected papers presented at the MIMS (Mediterranean Institute for the Mathematical Sciences) - GGTM (Geometry and Topology Grouping for the Maghreb) conference, held in memory of Mohammed Salah Baouendi, a most renowned figure in the field of several complex variables, who passed away in 2011. All research articles were written by leading experts, some of whom are prize winners in the fields of complex geometry, algebraic geometry and analysis. The book offers a valuable resource for all researchers interested in recent developments in analysis and geometry.