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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]:
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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2011, Issue 1(22), Pages 165–171 (Mi vsgtu875)  

This article is cited in 3 scientific papers (total in 3 papers)

Procedings of the 2nd International Conference "Mathematical Physics and its Applications"
Mathematical Physics

Theorem on the norm of elements of spinor groups

D. S. Shirokov

Dept. of Mathematical Physics, Steklov Mathematical Institute, Russian Academy of Sciences, Moscow

Abstract: 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, orthochronous group, orthochorous group

DOI: https://doi.org/10.14498/vsgtu875

Full text: PDF file (543 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
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Bibliographic databases:

UDC: 512.5
MSC: 15A66
Original article submitted 20/XII/2010
revision submitted – 17/II/2011

Citation: D. S. Shirokov, “Theorem on the norm of elements of spinor groups”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 1(22) (2011), 165–171

Citation in format AMSBIB
\Bibitem{Shi11}
\by D.~S.~Shirokov
\paper Theorem on the norm of elements of spinor groups
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2011
\vol 1(22)
\pages 165--171
\mathnet{http://mi.mathnet.ru/vsgtu875}
\crossref{https://doi.org/10.14498/vsgtu875}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. D. S. Shirokov, “Lektsii po algebram Klifforda i spinoram”, Lekts. kursy NOTs, 19, MIAN, M., 2012, 3–179  mathnet  crossref  zmath
    2. D. S. Shirokov, “Ispolzovanie obobschennoi teoremy Pauli dlya nechetnykh elementov algebry Klifforda dlya analiza svyazei mezhdu spinornymi i ortogonalnymi gruppami proizvolnykh razmernostei”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 1(30) (2013), 279–287  mathnet  crossref
    3. D. Shirokov, “Clifford algebras and their applications to Lie groups and spinors”, Geometry, Integrability and Quantization, 19 (2018), 11–53, arXiv: 1709.06608 [math-ph]  crossref  mathscinet  zmath  isi  scopus
  • Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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