Zur Darstellung der Klassischen Gruppen durch Clifford-Algebren

Let (V,K,Q) be a finite dimensional metric vector space, and let C(Q) be the corresponding Clifford algebra. In this paper, representations of the classical groups O_n(V,Q) and PO_n(V,Q) by C(Q) are given for the case of arbitrary rank and arbitrary characteristic. For example, the following is proved: If R is the domain of regularity of C(Q) with center Z_R then — apart from three exceptions — R/Z_R is isomorphic to O_n(V,Q), and ancorresponding result is obtained for PO_n (V,Q).