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Sibirskii Matematicheskii Zhurnal, 2013, Volume 54, Number 4, Pages 890–901 (Mi smj2464)  
This article is cited in 6 scientific papers (total in 6 papers)

Differentiably simple Jordan algebras

A. A. Popovab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia
Full-text PDF (346 kB) Citations (6)
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Abstract: We prove that each exceptional differentiably simple Jordan algebra over a field of characteristic 0 is an Albert ring whose elements satisfy a cubic equation with the coefficients in the center of the algebra. If the characteristic of the field is greater than 2 then such an algebra is the tensor product of its center and a central exceptional simple 27-dimensional Jordan algebra. Some remarks made on special algebras.
Keywords: Jordan algebra, derivation, differentiably simple algebra.
Received: 04.07.2012
English version:
Siberian Mathematical Journal, 2013, Volume 54, Issue 4, Pages 713–721
DOI: https://doi.org/10.1134/S0037446613040113
Bibliographic databases:
Document Type: Article
UDC: 512.554.7
Language: Russian
Citation: A. A. Popov, “Differentiably simple Jordan algebras”, Sibirsk. Mat. Zh., 54:4 (2013), 890–901; Siberian Math. J., 54:4 (2013), 713–721
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/smj/v54/i4/p890
    • This publication is cited in the following 6 articles:
    1. I. Kaygorodov, A. Lopatin, Yu. Popov, “The structure of simple noncommutative Jordan superalgebras”, Mediterr. J. Math., 15:2 (2018), 33  crossref  mathscinet  isi  scopus
    2. I. Kaygorodov, A. Lopatin, Yu. Popov, “Jordan algebras admitting derivations with invertible values”, Commun. Algebr., 46:1 (2018), 69–81  crossref  mathscinet  zmath  isi  scopus
    3. I. Kaygorodov, Yu. Popov, “A characterization of nilpotent nonassociative algebras by invertible Leibniz-derivations”, J. Algebra, 456 (2016), 323–347  crossref  mathscinet  zmath  isi  scopus
    4. I. Kaygorodov, A. Lopatin, Yu. Popov, “Conservative algebras of 2-dimensional algebras”, Linear Alg. Appl., 486 (2015), 255–274  crossref  mathscinet  zmath  isi  elib  scopus
    5. I. B. Kaygorodov, Yu. S. Popov, “Alternative algebras admitting derivations with invertible values and invertible derivations”, Izv. Math., 78:5 (2014), 922–936  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    6. V. N. Zhelyabin, M. E. Goncharov, “Primer differentsialno prostoi algebry Li, ne yavlyayuscheisya svobodnym modulem nad svoim tsentroidom”, Sib. elektron. matem. izv., 11 (2014), 915–920  mathnet
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