Permutation Groups, Algebras and Geometries will be the theme of the
CIMPA-African Mathematical School: Algebras, Geometries and Permutation Groups.
The school will be held at the University of KwaZulu-Natal, at the Howard College Campus in Durban, from
08 to 20 December 2019.
Recent research trends including :
The material will be provided in 6 mini-courses of 6 hours each. All mini-courses will be in English.
Topics
CIMPA-African Mathematical School: Algebras, Geometries and Permutation Groups.
The school will be held at the University of KwaZulu-Natal, at the Howard College Campus in Durban, from
08 to 20 December 2019.
Recent research trends including :
- interactions between finite groups and algebras,
- group algebras and codes,
- connections between representation theory of finite groups and linear codes
The material will be provided in 6 mini-courses of 6 hours each. All mini-courses will be in English.
Topics
- Jordan algebras. Special algebras for classical groups, spin factors,
- Hermitian matrices over quaternions and octonions.
- Idempotents in Jordan algebras. Peirce decomposition.
- Frobenius form and the general algebra structure.
- Abstract fusion rules, axial algebras. Monster algebra.
- Graded fusion rules and axial automorphisms.
- Code algebras, axial algebras and Vertex Operator Algebras
- Finite transitive/primitive groups
- The O'Nan-Scott theorem
- Representation theory of finite groups
- Fischer matrices and character tables of maximal subgroups of finite simple groups
- Permutation modules of finite groups
- Group Codes