PT EN

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

  • Representations of fundamental groups of surfaces
    Peter Gothen (CMUP)
    15:30, Room 2.5, UC Math. Dept.
    (Seminar)
    November 23, 2018
  • On the existence of solutions for inextensible string equations
    Ayk Telciyan (student)
    12:30, Room 2.5, UC Math. Dept.
    (Seminar)
    November 23, 2018
  • Boolean representable simplicial complexes
    Maria Inês Couto (student)
    12:00, Room 2.5, UC Math. Dept.
    (Seminar)
    November 23, 2018
  • Campanato spaces and applications in partial differential equations
    David Jesus (student)
    11:30, Room 2.5, UC Math. Dept.
    (Seminar)
    November 23, 2018
  • A mathematical model for a plant circadian oscillator
    Adérito Araújo (CMUC)
    14:00, Room 2.5, UC Math. Dept.
    (Seminar)
    November 28, 2018
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Defended Theses

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