Semisimple algebras and representations of finite groups
Period of duration of course
Basic knowledge of algebra. For third year undergraduate students.
• Finite algebras over fields. Modules.
• The Jacobson radical
• Semisimplicity. Wedderburn's structure theorem.
• Group algebras. Representations of finite group over algebraically closed fields. Characters and orthogonality.
• Central simple algebras and division algebras. The Brauer group of a field of a field.
• Applications to representations of finite groups over non algebraically closed fields.
Teaching abut semisimple algebras and representations of finite groups