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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2019, Volume 16, Pages 2110–2123
DOI: https://doi.org/10.33048/semi.2019.16.150 (Mi semr1191) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Mathematical logic, algebra and number theory

On the Cayley–Dickson process for dialgebras

A. P. Pozhidaevab

a Sobolev Institute of Mathematics, 4, Koptyuga ave., Novosibirsk, 630090, Russia
b Novosibirsk State University, 2, Pirogova str., Novosibirsk, 630090, Russia
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DOI: https://doi.org/10.33048/semi.2019.16.150
Abstract: We prove that the dialgebras, which are obtained by the Cayley–Dickson process from the two-dimensional commutative associative dialgebra ${\mathcal D}$, are disimple noncommutative Jordan dialgebras. Furthermore, a decomposition holds for them into the direct sum of a composition algebra and the equating ideal of the dialgebra.
Keywords: dialgebra, Cayley–Dickson process, flexible algebra, involution, noncommutative Jordan algebra, disimple dialgebra, composition algebra.
Funding agency Grant number
Russian Foundation for Basic Research 18-31-20004_Стабильность
The work is supported by RFBR (Grant 18-31-20004).
Received October 2, 2019, published December 27, 2019
Bibliographic databases:
Document Type: Article
UDC: 512.554
MSC: 17A15, 17A01
Language: English
Citation: A. P. Pozhidaev, “On the Cayley–Dickson process for dialgebras”, Sib. Èlektron. Mat. Izv., 16 (2019), 2110–2123
Citation in format AMSBIB
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\by A.~P.~Pozhidaev
\paper On the Cayley--Dickson process for dialgebras
\jour Sib. \`Elektron. Mat. Izv.
\yr 2019
\vol 16
\pages 2110--2123
\mathnet{http://mi.mathnet.ru/semr1191}
\crossref{https://doi.org/10.33048/semi.2019.16.150}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000509879000001}
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