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
In , 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.
Jordan superalgebra, $(-1,1)$-superalgebra, superalgebra of vector type, differentially simple algebra, algebra of polynomials, projective module.
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Siberian Advances in Mathematics, 2010, 20:3, 223–230
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
\paper Differential algebras and simple Jordan superalgebras
\jour Mat. Tr.
\jour Siberian Adv. Math.
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This publication is cited in the following articles:
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
V. N. Zhelyabin, “Jordan superalgebras of vector type and projective modules”, Siberian Math. J., 53:3 (2012), 450–460
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
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
S. O. Gorchinskiy, “Generation of modules and transcendence degree of zero-cycles”, Izv. Math., 77:4 (2013), 696–699
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
A. S. Zakharov, “Embedding Novikov–Poisson algebras in Novikov–Poisson algebras of vector type”, Algebra and Logic, 52:3 (2013), 236–249
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
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
V. N. Zhelyabin, A. S. Zakharov, “Some constructions for Jordan superalgebras with associative even part”, St. Petersburg Math. J., 28:2 (2017), 197–208
V. N. Zhelyabin, “Simple Jordan superalgebras with associative nil-semisimple even part”, Siberian Math. J., 57:6 (2016), 987–1001
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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