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Mat. Tr., 2009, Volume 12, Number 2, Pages 41–51 (Mi mt180)  

This article is cited in 12 scientific papers (total in 12 papers)

Differential algebras and simple Jordan superalgebras

V. N. Zhelyabinab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia

Abstract: In [14], a new example is constructed of a unital simple special Jordan superalgebra $J$ over the field of reals. It turns out that $J$ is a subsuperalgebra of a Jordan superalgebra of vector type but it cannot be isomorphic to a superalgebra of such a type. Moreover, the superalgebra of fractions of $J$ is isomorphic to a Jordan superalgebra of vector type. In the present article, we find a similar example of a Jordan superalgebra. It is constructed over a field of characteristic $0$ in which the equation $t^2+1=0$ has no solutions.

Key words: Jordan superalgebra, $(-1,1)$-superalgebra, superalgebra of vector type, differentially simple algebra, algebra of polynomials, projective module.

Full text: PDF file (165 kB)
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English version:
Siberian Advances in Mathematics, 2010, 20:3, 223–230

Bibliographic databases:

UDC: 512.554
Received: 14.09.2009

Citation: V. N. Zhelyabin, “Differential algebras and simple Jordan superalgebras”, Mat. Tr., 12:2 (2009), 41–51; Siberian Adv. Math., 20:3 (2010), 223–230

Citation in format AMSBIB
\Bibitem{Zhe09}
\by V.~N.~Zhelyabin
\paper Differential algebras and simple Jordan superalgebras
\jour Mat. Tr.
\yr 2009
\vol 12
\issue 2
\pages 41--51
\mathnet{http://mi.mathnet.ru/mt180}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2599424}
\transl
\jour Siberian Adv. Math.
\yr 2010
\vol 20
\issue 3
\pages 223--230
\crossref{https://doi.org/10.3103/S1055134410030077}


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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. V. N. Zhelyabin, “New examples of simple Jordan superalgebras over an arbitrary field of characteristic zero”, St. Petersburg Math. J., 24:4 (2013), 591–600  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    2. V. N. Zhelyabin, “Jordan superalgebras of vector type and projective modules”, Siberian Math. J., 53:3 (2012), 450–460  mathnet  crossref  mathscinet  isi
    3. Leidwanger S., Morier-Genoud S., “Superalgebras Associated to Riemann Surfaces: Jordan Algebras of Krichever-Novikov Type”, Int. Math. Res. Notices, 2012, no. 19, 4449–4474  crossref  mathscinet  zmath  isi  scopus
    4. V. N. Zhelyabin, “Examples of prime Jordan superalgebras of vector type and superalgebras of Cheng–Kac type”, Siberian Math. J., 54:1 (2013), 33–39  mathnet  crossref  mathscinet  isi
    5. S. O. Gorchinskiy, “Generation of modules and transcendence degree of zero-cycles”, Izv. Math., 77:4 (2013), 696–699  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    6. V. N. Zhelyabin, A. A. Popov, I. P. Shestakov, “The coordinate ring of an $n$-dimensional sphere and some examples of differentially simple algebras”, Algebra and Logic, 52:4 (2013), 277–289  mathnet  crossref  mathscinet  isi
    7. A. S. Zakharov, “Embedding Novikov–Poisson algebras in Novikov–Poisson algebras of vector type”, Algebra and Logic, 52:3 (2013), 236–249  mathnet  crossref  mathscinet  isi
    8. Leidwanger S., Morier-Genoud S., “a Short Survey of Lie Antialgebras”, 3Quantum: Algebra Geometry Information (Qqq Conference 2012), Journal of Physics Conference Series, 532, IOP Publishing Ltd, 2014, 012015  crossref  mathscinet  isi  scopus
    9. V. N. Zhelyabin, “$(-1,1)$-superalgebras of vector type: Jordan superalgebras of vector type and their universal envelopings”, Siberian Math. J., 56:3 (2015), 411–424  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    10. V. N. Zhelyabin, A. S. Zakharov, “Some constructions for Jordan superalgebras with associative even part”, St. Petersburg Math. J., 28:2 (2017), 197–208  mathnet  crossref  mathscinet  isi  elib
    11. V. N. Zhelyabin, “Simple Jordan superalgebras with associative nil-semisimple even part”, Siberian Math. J., 57:6 (2016), 987–1001  mathnet  crossref  crossref  isi  elib
    12. V. N. Zhelyabin, “Structure of some unital simple Jordan superalgebras with associative even part”, Siberian Math. J., 59:6 (2018), 1051–1062  mathnet  crossref  crossref  isi
  • Математические труды Siberian Advances in Mathematics
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