On some relations between spinor and orthogonal groups

P-Adic Numbers, Ultrametric Analysis, and Applications. 2011. Vol. 3. No. 3. P. 212–218.

Широков Д. С.

In this article we consider Clifford algebras over the field of real numbers of finite dimension. We define the operation of Hermitian conjugation for the elements of Clifford algebra. This operation allows us to define the structure of Euclidian space on the Clifford algebra. We consider pseudo-orthogonal group and its subgroups – special pseudo-orthogonal, orthochronous, orthochorous and special orthochronous groups. As we know, spinor groups are double covers of these orthogonal groups.We proved theorem that relates the norm of element of spinor group to the minor of matrix of the corresponding orthogonal group.

Ключевые слова: Clifford algebra, алгебра Клиффорда, spin groups, orthogonal groups, спинорные группы, ортогональные группы