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Sibirsk. Mat. Zh., 2004, Volume 45, Number 5, Pages 1046–1072 (Mi smj1119)  

This article is cited in 20 scientific papers (total in 20 papers)

Simple special Jordan superalgebras with associative even part

V. N. Zhelyabin, I. P. Shestakov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: We describe the simple special unital Jordan superalgebras with associative even part $A$ whose odd part $M$ is an associative module over $A$. We prove that each of these superalgebras, not isomorphic to a superalgebra of nondegenerate bilinear superform, is isomorphically embedded into a twisted Jordan superalgebra of vector type. We exhibit a new example of a simple special Jordan superalgebra. We also describe the superalgebras such that $M\cap[A,M]\ne0$.

Keywords: Jordan superalgebra, $(-1,1)$-superalgebra, twisted superalgebra of vector type, differentiably simple algebra, projective module, localization of module

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English version:
Siberian Mathematical Journal, 2004, 45:5, 860–882

Bibliographic databases:

UDC: 512.554
Received: 09.02.2004

Citation: V. N. Zhelyabin, I. P. Shestakov, “Simple special Jordan superalgebras with associative even part”, Sibirsk. Mat. Zh., 45:5 (2004), 1046–1072; Siberian Math. J., 45:5 (2004), 860–882

Citation in format AMSBIB
\by V.~N.~Zhelyabin, I.~P.~Shestakov
\paper Simple special Jordan superalgebras with associative even part
\jour Sibirsk. Mat. Zh.
\yr 2004
\vol 45
\issue 5
\pages 1046--1072
\jour Siberian Math. J.
\yr 2004
\vol 45
\issue 5
\pages 860--882

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    This publication is cited in the following articles:
    1. V. N. Zhelyabin, A. S. Tikhov, “Novikov–Poisson algebras and associative commutative derivation algebras”, Algebra and Logic, 47:2 (2008), 107–117  mathnet  crossref  mathscinet  zmath  isi
    2. V. N. Zhelyabin, “Differential algebras and simple Jordan superalgebras”, Siberian Adv. Math., 20:3 (2010), 223–230  mathnet  crossref  mathscinet
    3. 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
    4. V. N. Zhelyabin, “Jordan superalgebras of vector type and projective modules”, Siberian Math. J., 53:3 (2012), 450–460  mathnet  crossref  mathscinet  isi
    5. 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
    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. S. V. Pchelintsev, O. V. Shashkov, “Simple finite-dimensional right-alternative superalgebras of Abelian type of characteristic zero”, Izv. Math., 79:3 (2015), 554–580  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    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. Pchelintsev S.V., Shestakov I.P., “Prime (-1,1) and Jordan Monsters and Superalgebras of Vector Type”, J. Algebra, 423 (2015), 54–86  crossref  mathscinet  zmath  isi  elib  scopus
    11. da Silva J.P., Murakami L.S.I., Shestakov I., “on Right Alternative Superalgebras”, Commun. Algebr., 44:1 (2016), 240–252  crossref  mathscinet  zmath  isi  scopus
    12. 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
    13. S. V. Pchelintsev, O. V. Shashkov, “Simple right alternative superalgebras of Abelian type whose even part is a field”, Izv. Math., 80:6 (2016), 1231–1241  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    14. 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
    15. S. V. Pchelintsev, O. V. Shashkov, “Simple finite-dimensional right-alternative unital superalgebras with associative-commutative even part over a field of characteristic zero”, Izv. Math., 82:3 (2018), 578–595  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    16. 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  elib
    17. V. N. Zhelyabin, “Dopolnenie k teoreme Bloka i k teoreme Popova o differentsialno prostykh algebrakh”, Sib. elektron. matem. izv., 16 (2019), 1375–1384  mathnet  crossref
    18. Carotenuto A., Dabrowski L., Dubois-Violette M., “Differential Calculus on Jordan Algebras and Jordan Modules”, Lett. Math. Phys., 109:1 (2019), 113–133  crossref  mathscinet  zmath  isi  scopus
    19. V. N. Zhelyabin, “Vlozhenie iordanovykh superalgebr v superalgebry iordanovykh skobok”, Sib. matem. zhurn., 61:1 (2020), 78–95  mathnet  crossref
    20. V. N. Zhelyabin, A. S. Zakharov, “Superalgebry iordanovykh skobok, opredelennye $n$-mernoi sferoi”, Sib. matem. zhurn., 61:4 (2020), 803–822  mathnet  crossref
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