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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2023, Volume 20, Issue 2, Pages 833–846
DOI: https://doi.org/10.33048/semi.2023.20.050 (Mi semr1613) 		 
Mathematical logic, algebra and number theory

Quasi-definite primitive axial algebras of Jordan type half

I. B. Gorshkov, V. Yu. Gubarev

Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia
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DOI: https://doi.org/10.33048/semi.2023.20.050
Abstract: Axial algebras are commutative nonassociative algebras generated by a finite set of primitive idempotents whose action on an algebra is semisimple, and the fusion laws on the products between eigenvectors for these idempotents are fulfilled. We find the sufficient conditions in terms of the Frobenius form and the properties of idempotents under which an axial algebra of Jordan type half is unital.
Keywords: axial algebra of Jordan type, Frobenius form, semisimplicity.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-15-2022-281
The work is supported by Mathematical Center in Akademgorodok under agreement No. 075-15-2022-281 with the Ministry of Science and Higher Education of the Russian Federation.
Received April 20, 2023, published October 20, 2023
Document Type: Article
UDC: 512.554
MSC: 17A60
Language: English
Citation: I. B. Gorshkov, V. Yu. Gubarev, “Quasi-definite primitive axial algebras of Jordan type half”, Sib. Èlektron. Mat. Izv., 20:2 (2023), 833–846
Citation in format AMSBIB
\Bibitem{GorGub23}
\by I.~B.~Gorshkov, V.~Yu.~Gubarev
\paper Quasi-definite primitive axial algebras of Jordan type half
\jour Sib. \`Elektron. Mat. Izv.
\yr 2023
\vol 20
\issue 2
\pages 833--846
\mathnet{http://mi.mathnet.ru/semr1613}
\crossref{https://doi.org/10.33048/semi.2023.20.050}
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