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

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.

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English version:
Siberian Advances in Mathematics, 2010, 20:3, 223–230

Bibliographic databases:

UDC: 512.554

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
2. V. N. Zhelyabin, “Jordan superalgebras of vector type and projective modules”, Siberian Math. J., 53:3 (2012), 450–460
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
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
5. S. O. Gorchinskiy, “Generation of modules and transcendence degree of zero-cycles”, Izv. Math., 77:4 (2013), 696–699
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
7. A. S. Zakharov, “Embedding Novikov–Poisson algebras in Novikov–Poisson algebras of vector type”, Algebra and Logic, 52:3 (2013), 236–249
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
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
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
11. V. N. Zhelyabin, “Simple Jordan superalgebras with associative nil-semisimple even part”, Siberian Math. J., 57:6 (2016), 987–1001
12. V. N. Zhelyabin, “Structure of some unital simple Jordan superalgebras with associative even part”, Siberian Math. J., 59:6 (2018), 1051–1062
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