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
Ali Baklouti is a Full Professor of Mathematics at the University of Sfax, Tunisia. He earned his Ph.D. in Mathematics from the University of Metz, France, in 1995. He served as Vice-President of the University of Sfax from December 2020 to July 2024 and held the position of President of the Tunisian Mathematical Society for two consecutive terms (April 2016-March 2019 and April 2019-March 2023). Since January 2012, he has been the Deputy Director of the Mediterranean Institute of Mathematical Sciences, an institution he co-founded that same year. In December 2016, he was elected as a permanent member of the Tunisian Academy of Sciences, Letters, and Arts.
Professor Baklouti has received numerous prestigious awards, including the AMU-PaCOM 2022 Award and Medal, Category A in Mathematics, and the Royal Society Africa Prize 2024. In the same year, he was also honored with the Order of Merit for Education and Teaching by the President of Tunisia. He is also appointed to be the holder of the "Chair Pays de Sud" for 2026 in Mathematics, CIRM-France.
He currently serves as Co-Editor-in-Chief of the Tunisian Journal of Mathematics (published by MSP, USA) and as Editor-in-Chief of Advances in Pure and Applied Mathematics
(published by ISTE, UK). Additionally, he is a member of the editorial boards of other several journals, including the Graduate Journal of Mathematics (MIMS), and the Arabian Journal of Mathematics.
Hidenori Fujiwara is an Emeritus Professor of Kinki University, Japan. He had been a Full Professor of Kinki University for 26 years and retired in 2013. He received his Ph.D. in Mathematics from Tokyo University (Japan) in1977. He studies the unitary representations of solvable Lie groups and the harmonic analysis on solvable homogeneous spaces. He published over 40 papers in peer-reviewed international journals, as well as two books.
Jean Ludwig is currently Professeur émérite at the Université de Lorraine, France. He received his Ph.D. in Mathematics from the University of Bielefeld (Germany) in 1976 and his habilitation in 1979. He was a professor of Metz University (France) from 1990 to 2014. He had 13 PHD students, and he published over 100 papers in peer-reviewed international journals and proceedings and acted as a co-editor of the Journal of Lie Theory. He had been Directeur du Labaoratoire LMAM for 3 years and had many administrative duties at the Department and UFR level at the University of Bielefeld and Metz.
