Theorem on the norm of elements of spinor groups


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.

About the authors

Dmitry S Shirokov

Steklov Mathematical Institute, Russian Academy of Sciences

аспирант, отд. математической физики; Математический институт им. В. А. Стеклова РАН; Steklov Mathematical Institute, Russian Academy of Sciences


  1. Lounesto P. Clifford algebras and spinors / L.M.S. Lecture Notes. Vol. 239. Cambridge: Cambridge Univ. Press, 1997. 306 pp.
  2. Марчук Н. Г. Уравнения теории поля и алгебры Клиффорда. М.-Ижевск: НИЦ РХД, 2009. 304 с.
  3. Marchuk N. G., Shirokov D. S. Unitary spaces on Clifford algebras // Adv. in Appl. Cliff. Alg., 2008. Vol. 18, no. 2. Pp. 237-254.
  4. Широков Д. С. Классификация элементов алгебр Клиффорда по кватернионным типам // ДАН, 2009. Т. 427, № 6. С. 758-760
  5. Benn I. M., Tucker R. W. An Introduction to Spinors and Geometry with Applications in Physics. Bristol: IOP Publishing Ltd, 1987. 358 pp.
  6. Гантмахер Ф. Р. Теория матриц. М.: Наука, 1988. 549 с.



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