商品描述
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
商品描述(中文翻譯)
《表示理論與 C*-代數》專注於可解李群的表示理論及其相關的非交換性調和分析，包括 C*-代數的研究。書中包含了長期以來在該理論中的問題的完整證明，包括幾個多項式猜想和原始零理想的描述。它深入研究了這些結構性特徵，使用軌道方法對單位表示進行分類，以及其背後的代數和分析框架。
本書最適合專攻李理論、非交換幾何、泛函分析、算子代數和理論物理的博士生、博士後研究員和研究人員。
**特色**
- 在可解和指數李群環境中，對多項式猜想（Corwin-Greenleaf 和 Duflo）的完整解決方案
- 在指數環境中，對於交織算子和原始理想結構的長期問題的完整結果
- 基於新方法的 Casimir 元素的綜合分析及其在幾個相關問題中的角色
- 通過使用傅立葉變換和譜分析的方法，詳細研究可解李群的 C*-代數
- 豐富的例子和反例，包括海森堡群、線狀群和 G6 群
- 在表示理論中，古典與現代方法之間的橋樑，並應用於調和分析和數學物理
作者簡介
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.
作者簡介(中文翻譯)
阿里·巴克盧提是突尼西亞斯法克斯大學的數學全職教授。他於1995年在法國梅斯大學獲得數學博士學位。從2020年12月到2024年7月，他擔任斯法克斯大學的副校長，並連任突尼西亞數學學會會長兩屆（2016年4月至2019年3月及2019年4月至2023年3月）。自2012年1月以來，他一直擔任地中海數學科學研究所的副所長，該機構是他在同年共同創立的。2016年12月，他被選為突尼西亞科學、文學和藝術學院的常任成員。
巴克盧提教授獲得了多項著名獎項，包括2022年AMU-PaCOM數學類別A獎和獎章，以及2024年英國皇家學會非洲獎。同年，他還獲得了突尼西亞總統頒發的教育和教學功勳勳章。他還被任命為2026年法國CIRM數學“南方國家講座”的持有者。
他目前擔任突尼西亞數學期刊（由美國MSP出版）的共同主編，以及《純數學與應用數學進展》（由英國ISTE出版）的主編。此外，他還是其他幾本期刊的編輯委員會成員，包括數學研究生期刊（MIMS）和阿拉伯數學期刊。
藤原秀則是日本近畿大學的名譽教授。他在近畿大學擔任全職教授26年，並於2013年退休。他於1977年在東京大學（日本）獲得數學博士學位。他研究可解李群的單位表示及可解均勻空間上的調和分析。他在國際同行評審期刊上發表了40多篇論文，以及兩本書籍。
讓·路德維希目前是法國洛林大學的名譽教授。他於1976年在德國比勒費爾德大學獲得數學博士學位，並於1979年獲得資格認證。他於1990年至2014年擔任梅斯大學的教授。他指導了13位博士生，並在國際同行評審期刊和會議上發表了100多篇論文，並擔任《李理論期刊》的共同編輯。他曾擔任LMAM實驗室主任3年，並在比勒費爾德大學和梅斯大學的系和UFR層級擔任多項行政職務。
