Representations of Generalized Clifford Algebras

          @misc{ pirsa_PIRSA:10050037,
            doi = {10.48660/10050037},
            url = {https://pirsa.org/10050037},
            author = {Coskun, Emre},
            keywords = {},
            language = {en},
            title = {Representations of Generalized Clifford Algebras},
            publisher = {Perimeter Institute},
            year = {2010},
            month = {may},
            note = {PIRSA:10050037 see, \url{https://pirsa.org}}
          }
          

Abstract

Clifford algebras arose in Dirac's work on the relativistic wave equation in quantum mechanics. Using the Clifford algebra associated to a quadratic form on a finite dimensional vector space, one can reduce the relativistic wave equation, a PDE of order two, to a system of linear PDEs. Similarly, one can use matrix representations of generalized (i.e. higher degree) Clifford algebras to reduce a PDE of higher degree. These generalized Clifford algebras have been the subject of ongoing research since late 1980s. In this talk, we will discuss generalized Clifford algebras, known results about their representations, and results of ongoing work in this direction.