Helena Albuquerque

Departmento de Matemática, Universidade de Coimbra

Cayley Algebras and Clifford Algebras as deformed group algebras
Non-associative graded algebras were introduced in the 80's and have interested mathematicians and physicists. We show in this conference that Clifford algebras and Cayley algebras (Octonions, Quaternions...) are a twisting of the group algebra $(Z_2)^n$ in the quasitensor category of representations of a quasi-Hopf algebra associated to a 3-group cocycle. Applications from some fields in Theoretical Physics are presented.