Represantations of real Clifford algebras

ABSTRACT Master of Science Thesis REPRESANTATİONS OF REAL CLIFFORD ALGEBRAS Şenay KARAPAZAR Anadolu University Graduate School of Natural and Applied Sciences Mathematics Program Supervisor: Yrd.Doç.Dr. Nedim DE?İRMENCİ 2004, 149 Pages In this thesis Real Clifford algebras and their represantations are studied. In the first two chapters symmetric bilinear forms and tensor product which are necessary to define Clifford algebras are given. In the third chapter Clifford algebras on the finite-dimensional real vector spaces are defined and their some properties are obtained. In the fourth chapter the table of matrix algebras which become isomorphic of non-degenerate Clifford algebras on Rn is given. Although this table was generally known, there are no explicit expressions of these isomorphisms in literature. In the fifth chapter, Clear expressions of the isomorphisms in the mentioned on table is given and thus a method is developed to obtain an isomorphism from a non-degenerate Clifford algebra on Rn to related matrix algebra. In the sixth and seventh chapter represantations of non-degenerate Clifford algebras were given. In the last chapter degenerate Clifford algebras are mentioned. Keywords: Symmetric bilinear form, Quadratic form, Tensor product, Clifford algebra, Represantation of algebra 11