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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.], 2015, Volume 19, Number 1, Pages 117–135 (Mi vsgtu1387)  

This article is cited in 2 scientific papers (total in 2 papers)

Differential Equations and Mathematical Physics

Contractions on ranks and quaternion types in Clifford algebras

D. S. Shirokovab

a A. A. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, 127994, Russian Federation
b Bauman Moscow State Technical University, Moscow, 105005, Russian Federation

Abstract: In this paper we consider expressions in real and complex Clifford algebras, which we call contractions or averaging. We consider contractions of arbitrary Clifford algebra element. Each contraction is a sum of several summands with different basis elements of Clifford algebra. We consider even and odd contractions, contractions on ranks and contractions on quaternion types. We present relation between these contractions and projection operations onto fixed subspaces of Clifford algebras - even and odd subspaces, subspaces of fixed ranks and subspaces of fixed quaternion types. Using method of contractions we present solutions of system of commutator equations in Clifford algebras. The cases of commutator and anticommutator are the most important. These results can be used in the study of different field theory equations, for example, Yang-Mills equations, primitive field equation and others.

Keywords: Clifford algebras, contractions, projection operations, quaternion type

Funding Agency Grant Number
Russian Science Foundation 14-11-00687
This work was supported by Russian Science Foundation (RSF 14–11–00687, Steklov Mathematical Institute).


DOI: https://doi.org/10.14498/vsgtu1387

Full text: PDF file (838 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
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Bibliographic databases:

UDC: 517.958
MSC: 15A66, 70S15
Original article submitted 15/XII/2014
revision submitted – 17/II/2014

Citation: D. S. Shirokov, “Contractions on ranks and quaternion types in Clifford algebras”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 19:1 (2015), 117–135

Citation in format AMSBIB
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\by D.~S.~Shirokov
\paper Contractions on ranks and quaternion types in Clifford algebras
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2015
\vol 19
\issue 1
\pages 117--135
\mathnet{http://mi.mathnet.ru/vsgtu1387}
\crossref{https://doi.org/10.14498/vsgtu1387}
\zmath{https://zbmath.org/?q=an:06968952}
\elib{http://elibrary.ru/item.asp?id=23681746}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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
    2. D. Shirokov, “Calculation of Elements of Spin Groups Using Method of Averaging in Clifford’s Geometric Algebra”, Advances in Applied Clifford Algebras, 29:3 (2019), 50, arXiv: 1901.09405 [math-ph]  crossref  isi  scopus
  • Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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