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Noncommutative Algebra

Program

The syllabus will vary from year to year but the core syllabus is
- Division rings: Quaternions, Cayley-Dickson construction.
- Wedderburn-Artin Theory: matrix rings over division rings and semisimple modules.
- Tensor products and categories.
- Algebras presented by generators and relations.
- Simple algebras: Weyl algebras, central simple algebras, Brauer group.

Further topics (an uncomplete list):
- Non-commutative polynomial rings: skew-polynomial rings, differential operator algebras
- Lie algebras and their enveloping algebras
- basic facts on Hopf algebras: Frobenius algebras, Maschke theorem, Noetherian Hopf algebras
- Noetherian ring theory: non-commutative localization and Goldie's theorem
- basic facts of homological algebra.

Research and Events

Events

  • There is no information available on this topic.
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Defended Theses

  • Numerical semigroups: a conjecture of Wilf and related topics
      Neeraj Kumar (July 2025)
      Manuel Delgado
      Claude Marion
  • Dynamics of vector fields with univalued solutions
      Laura Rosales Ortiz (June 2025)
      Helena Reis
      Júlio Rebelo (Université Toulouse III)
  • Regular transitions of physical measures in nonuniformly hyperbolic systems
      Odaudu Reuben Etubi (April 2025)
      José Ferreira Alves
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