International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 78613, 13 pages
doi:10.1155/IJMMS/2006/78613
Explicit isomorphisms of real Clifford algebras
Department of Mathematics, Faculty of Science, Anadolu University, Eskisehir 26470, Turkey
Received 13 March 2005; Revised 6 January 2006; Accepted 27 February 2006
Copyright © 2006 N. Değırmencı and Ş. Karapazar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
It is well known that the Clifford algebra Clp,q associated
to a nondegenerate quadratic form on ℝn (n=p+q) is isomorphic to a matrix algebra K(m) or direct sum K(m)⊕K(m) of matrix algebras, where K=ℝ,ℂ,ℍ. On the other hand, there are
no explicit expressions for these isomorphisms in literature. In
this work, we give a method for the explicit construction of these
isomorphisms.