Geodesic
Theorem on the norm of elements of spinor groups
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 1 (2011), pp. 165-171

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In this article we consider Clifford's algebra over the field of real numbers of finite dimension. We define the operation of Hermitian conjugation for the elements of Clifford's 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 known, spinor groups are double covers of these orthogonal groups. We proved a theorem that relates the norm of element of spinor group with the minor of matrix of the orthogonal group.
Keywords: Clifford's algebra, spinor groups, orthogonal groups
Mots-clés : orthochronous group, orthochorous group. 
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     title = {Theorem on the norm of elements of spinor groups},
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D. S. Shirokov. Theorem on the norm of elements of spinor groups. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 1 (2011), pp. 165-171. http://geodesic.mathdoc.fr/item/VSGTU_2011_1_a21/