U (h)-finitely generated g-modules and Coherent families

Sep 8, 2026

U (h)-finitely generated g-modules and coherent families investigate algebraic structures arising from module theory in the setting of Lie algebras, focusing on the interplay between semisimple Lie algebras and associative algebra frameworks. The dissertation emphasizes results and arguments developed throughout the doctorate, culminating in a corrected thesis version after defense feedback. It is formally presented as a joint-supervision doctorate in mathematics between two institutions, with explicit supervision by Iryna Kashuba and Olivier Mathieu.

LanguageEnglish

CategoryResearch & Report

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Pages157

Reading Time6 h 36 min

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ÁLGEBRAS DE LIE SEMISSIMPLES

ANÉIS E ÁLGEBRAS ASSOCIATIVOS

MÓDULOS

U (h)-finitely generated g-modulesand coherent families Eduardo Monteiro Mendonça Dissertation Submitted to Institute of Mathematics and Statistics of University of São Paulo and Institut Camille Jordan of Université Claude Bernard Lyon 1 in Partial Fulfilment of the Requirements for the Degree of Doctor of Philosofy Doctorate in Mathematics Supervisor: Prof. Dr. Olivier Mathieu Supervisor: Prof. Dr. Iryna Kashuba During the development of this work, the author received the following financial assistance: Coordination of Superior Level Staff Improvement (CAPES), Finance Code 001, grant \#2020/14313-4, São Paulo Research Foundation (FAPESP), grant \#2022/05915-6, São Paulo Research Foundation (FAPESP), contract “Cohomologie des algèbres de Jordan”, LabEx Milyon. São Paulo, June 2025 U (h)-finitely generated g-modules and Coherent families This version of the thesis contains the corrections and changes suggested by the Judging Committee during the defense of the original version of the work, held on 07/07/2025 . A copy of the original version is available at Institute of Mathematics and Statistics, University of São Paulo. Judging Committee: • Prof. Dr. Adriano Adrega Moura-UNICAMP, Brazil • Prof. Dr. Dessislava Hristoc-UNICAMP, Brazil • Prof. Dr. Laurent Rigal -USPN, France • Prof. Dr. Lucia Satie Ikemoto-IME-USP, Brazil • Prof. Dr. Nicolas Andriuskewtisch-UNC, Argentina • Prof. Dr. Olivier Mathieu-ICJ-UCBL, France • Prof. Dr. Philippe Malbos-ICJ-UCBL, France Ficha catalográfica elaborada com dados inseridos pelo(a) autor(a) Biblioteca Carlos Benjamin de Lyra Instituto de Matemática e Estatística Universidade de São Paulo Mendonça, Eduardo Monteiro U(h)-finitely generated g-modules and coherent families / Eduardo Monteiro Mendonça; orientadora, Iryna Kashuba; coorientador, Olivier Mathieu . - São Paulo, 2025 . 141 p . Tese (Doutorado) -Programa de Pós-Graduação em Matemática / Instituto de Matemática e Estatística / Universidade de São Paulo . Bibliografia Versão corrigida 1 . ÁLGEBRAS DE LIE SEMISSIMPLES . 2 . ANÉIS E ÁLGEBRAS ASSOCIATIVOS . 3 . MÓDULOS . I . Kashuba, Iryna . II . Título . Bibliotecárias do Serviço de Informação e Biblioteca Carlos Benjamin de Lyra do IME-USP, responsáveis pela estrutura de catalogação da publicação de acordo com a AACR2: Maria Lúcia Ribeiro CRB-8/2766; Stela do Nascimento Madruga CRB 8/7534 . Acknowledgment Completing my doctorate and this PhD thesis has been a long and challenging journey that would not have been possible without the support of many people. Their guidance, kindness, and encouragement not only helped me overcome obstacles, but also made these past years truly rewarding and memorable. I am deeply thankful to all those who have touched my life during this process and who have contributed to my academic, professional, and personal growth. First, I would like to express my deepest gratitude to my supervisors, Iryna Kashuba and Olivier Mathieu. I have been Iryna’s student since my bachelor’s studies, which gave me the opportunity to build not only a strong academic relationship but also a deep personal bond with her. Over the years, I have found in her not just a mentor but also a true friend. She has always believed in my abilities, independence in mathematics, and sense of responsibility. With her constant trust and dedication, she created opportunities that were essential for both my personal and professional growth. Her support and wisdom taught me lessons that will be with me for life. At the same time, I am immensely grateful to Olivier, who first introduced me to the field of research that I now mostly enjoy. From him, I learned important lessons about how to approach mathematics: to always look at the bigger picture, to seek connections within different areas of mathematics in order to build deeper intuition, and to never settle for the first proof but to search for alternative approa

FAQs

What is the dissertation’s main topic?

The dissertation studies U (h)-finitely generated g-modules and coherent families, focusing on related algebraic structures in module theory.

Who supervised the PhD work?

The supervisors are Prof. Dr. Iryna Kashuba and Prof. Dr. Olivier Mathieu, with joint supervision between the involved institutions.

Was the thesis revised after the defense?

Yes. The document states that this version contains corrections and changes suggested by the Judging Committee after the defense held on 07/07/2025.

Sep 8, 2026

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