The use of the generalized Pauli's theorem for odd elements of Clifford algebra to analyze relations between spin and orthogonal groups of arbitrary dimensions

The use of the generalized Pauli's theorem for odd elements of Clifford algebra to analyze relations between spin and orthogonal groups of arbitrary dimensions

In the present paper we consider the use of generalized Pauli's theorem to prove the theorem about double cover of orthogonal groups by spin groups. We prove theorems about double cover of orthochronous, othochorous, special and special orthochronous groups by corresponding spin groups. We sho...

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Main Author: D. S. Shirokov
Format: Article
Language:English
Published: Samara State Technical University 2013-03-01
Series:Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki
Online Access:http://mi.mathnet.ru/eng/vsgtu1176
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spelling doaj-c1d00897ab034bc3ae079eb7bcc771172020-11-25T02:12:16ZengSamara State Technical UniversityVestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki1991-86152310-70812013-03-011(30)27928710.14498/vsgtu1176 The use of the generalized Pauli's theorem for odd elements of Clifford algebra to analyze relations between spin and orthogonal groups of arbitrary dimensionsD. S. Shirokov In the present paper we consider the use of generalized Pauli's theorem to prove the theorem about double cover of orthogonal groups by spin groups. We prove theorems about double cover of orthochronous, othochorous, special and special orthochronous groups by corresponding spin groups. We show the difference between the approaches using adjoint action and twisted adjoint action.http://mi.mathnet.ru/eng/vsgtu1176
collection DOAJ
language English
format Article
sources DOAJ
author D. S. Shirokov
spellingShingle D. S. Shirokov
The use of the generalized Pauli's theorem for odd elements of Clifford algebra to analyze relations between spin and orthogonal groups of arbitrary dimensions
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki
author_facet D. S. Shirokov
author_sort D. S. Shirokov
title The use of the generalized Pauli's theorem for odd elements of Clifford algebra to analyze relations between spin and orthogonal groups of arbitrary dimensions
title_short The use of the generalized Pauli's theorem for odd elements of Clifford algebra to analyze relations between spin and orthogonal groups of arbitrary dimensions
title_full The use of the generalized Pauli's theorem for odd elements of Clifford algebra to analyze relations between spin and orthogonal groups of arbitrary dimensions
title_fullStr The use of the generalized Pauli's theorem for odd elements of Clifford algebra to analyze relations between spin and orthogonal groups of arbitrary dimensions
title_full_unstemmed The use of the generalized Pauli's theorem for odd elements of Clifford algebra to analyze relations between spin and orthogonal groups of arbitrary dimensions
title_sort use of the generalized pauli's theorem for odd elements of clifford algebra to analyze relations between spin and orthogonal groups of arbitrary dimensions
publisher Samara State Technical University
series Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki
issn 1991-8615
2310-7081
publishDate 2013-03-01
description In the present paper we consider the use of generalized Pauli's theorem to prove the theorem about double cover of orthogonal groups by spin groups. We prove theorems about double cover of orthochronous, othochorous, special and special orthochronous groups by corresponding spin groups. We show the difference between the approaches using adjoint action and twisted adjoint action.
url http://mi.mathnet.ru/eng/vsgtu1176
work_keys_str_mv AT dsshirokov theuseofthegeneralizedpaulistheoremforoddelementsofcliffordalgebratoanalyzerelationsbetweenspinandorthogonalgroupsofarbitrarydimensions
AT dsshirokov useofthegeneralizedpaulistheoremforoddelementsofcliffordalgebratoanalyzerelationsbetweenspinandorthogonalgroupsofarbitrarydimensions
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