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δ-Superderivations of semisimple finite-dimensional Jordan superalgebras

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Abstract

In the paper, a complete description of the δ-derivations and the δ-superderivations of semisimple finite-dimensional Jordan superalgebras over an algebraically closed field of characteristic p ≠ 2 is given. In particular, new examples of nontrivial (1/2)-derivations and odd (1/2)-superderivations are given that are not operators of right multiplication by an element of the superalgebra.

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References

  1. N. C. Hopkins, “Generalized derivations of nonassociative algebras,” Nova J. Math. Game Theory Algebra 5(3), 215–224 (1996).

    MathSciNet  MATH  Google Scholar 

  2. V. T. Filippov, “On Lie algebras that satisfy an identity of degree 5,” Algebra Logika 34(6), 681–705 (1995) [Algebra Logic 34 (6), 379–394 (1995) (1996)].

    MATH  Google Scholar 

  3. V. T. Filippov, “On δ-derivations of Lie algebras,” Sibirsk. Mat. Zh. 39(6), 1409–1422 (1998) [Siberian Math. J. 39 (6), 1218–1230 (1998)].

    MathSciNet  MATH  Google Scholar 

  4. V. T. Filippov, “δ-derivations of prime Lie algebras,” Sibirsk. Mat. Zh. 40(1), 201–213 (1999) [Siberian Math. J. 40 (1), 174–184 (1999)].

    MathSciNet  MATH  Google Scholar 

  5. V. T. Filippov, “On δ-derivations of prime alternative and Maltsev algebras,” Algebra Logika 39(5), 618–625 (2000) [Algebra Logic 39 (5), 354–358 (2000)].

    Article  MATH  Google Scholar 

  6. I. B. Kaygorodov, “On δ-derivations of simple finite-dimensional Jordan superalgebras,” Algebra Logika 46(5), 585–605 (2007) [Algebra Logic 46 (5), 318–329 (2007)].

    Article  MathSciNet  Google Scholar 

  7. I. B. Kaygorodov, “On δ-derivations of classical Lie superalgebras,” Sibirsk. Mat. Zh. 50(3), 547–565 (2009) Siberian Math. J. 50 (3), 434–449 (2009)].

    Article  Google Scholar 

  8. I. B. Kaygorodov, “on δ-superderivations of simple finite-dimensional Jordan and Lie superalgebras,” Algebra Logika 49(2), 195–215 (2010) [Algebra Logic 49 (2), 130–144 (2010)].

    MathSciNet  Google Scholar 

  9. I. B. Kaygorodov, “Generalized Kantor Double,” Vestnik Samarsk. Gos. Univ. 78(4), 42–50 (2010) [in Russian].

    Google Scholar 

  10. V. N. Zhelyabin and I. B. Kaygorodov, “On δ-superderivations of simple superalgebras of Jordan brackets,” Algebra i Analiz 23(4), 40–58 (2011) [in Russian].

    Google Scholar 

  11. P. Zusmanovich, “On δ-derivations of Lie algebras and superalgebras,” J. Algebra 324(12), 3470–3486 (2010).

    Article  MathSciNet  MATH  Google Scholar 

  12. I. B. Kaygorodov, “On δ-derivations of algebras and superalgebras,” in Problems in Theoretical and Applied Mathematics, Proceedings of the 41th All-Russia Youth School-Conference (Izd. Ucheb.-Metod. Tsentr UPI, Ekaterinburg, 2010), pp. 27–33, http://home.imm.uran.ru/digas/School-2010-A5.pdf [in Russian].

    Google Scholar 

  13. I. L. Kantor, “Jordan and Lie superalgebras determined by a Poisson algebra,” in Algebra and Analysis (Tomsk, 1989) (Izd. TomskGos. Univ., Tomsk, 1989), pp. 55–80 [Amer. Math. Soc. Transl., Ser. 2, Vol. 151, 1992].

    Google Scholar 

  14. V. G. Kac, “Classification of simple Z-graded Lie superalgebras and simple Jordan superalgebras,” Comm. Algebra 5(13), 1375–1400 (1977).

    Article  MathSciNet  MATH  Google Scholar 

  15. M. L. Racine and E. I. Zel’manov, “Simple Jordan superalgebras with semisimple even part,” J. Algebra 270(2), 374–444 (2003).

    Article  MathSciNet  MATH  Google Scholar 

  16. C. Martinez and E. Zelmanov, “Simple finite-dimensional Jordan superalgebras of prime characteristic,” J. Algebra 236(2), 575–629 (2001).

    Article  MathSciNet  MATH  Google Scholar 

  17. E. Zelmanov, “Semisimple finite dimensional Jordan superalgebras,” in Lie Algebras, Rings, and Related Topics, Taiwan, January 11–17, 1997 (Springer, Hong Kong, 2000), pp. 227–243.

    Google Scholar 

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk State University, Novosibirsk, Russia

    I. B. Kaygorodov

  2. Universidade de São Paulo, São Paulo, Brazil

    I. B. Kaygorodov

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  1. I. B. Kaygorodov
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Correspondence to I. B. Kaygorodov.

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Original Russian Text © I. B. Kaygorodov, 2012, published in Matematicheskie Zametki, 2012, Vol. 91, No. 2, pp. 200–213.

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Kaygorodov, I.B. δ-Superderivations of semisimple finite-dimensional Jordan superalgebras. Math Notes 91, 187–197 (2012). https://doi.org/10.1134/S0001434612010208

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  • DOI: https://doi.org/10.1134/S0001434612010208

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