Geodesic
$\delta$-Superderivations of simple finite-dimensional Jordan and Lie superalgebras
Algebra i logika, Tome 49 (2010) no. 2, pp. 195-215.

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We introduce the concept of a $\delta$-superderivation of a superalgebra. $\delta$-Derivations of Cartan-type Lie superalgebras are treated, as well as $\delta$-superderivations of simple finite-dimensional Lie superalgebras and Jordan superalgebras over an algebraically closed field of characteristic 0. We give a complete description of $\frac12$-derivations for Cartan-type Lie superalgebras. It is proved that nontrivial $\delta$-(super)derivations are missing on the given classes of superalgebras, and as a consequence, $\delta$-superderivations are shown to be trivial on simple finite-dimensional noncommutative Jordan superalgebras of degree at least 2 over an algebraically closed field of characteristic 0. Also we consider $\delta$-derivations of unital flexible and semisimple finite-dimensional Jordan algebras over a field of characteristic not 2.
Keywords: $\delta$-superderivation, Cartan-type Lie superalgebra, simple finite-dimensional Lie superalgebra, Jordan superalgebra. 
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I. B. Kaigorodov. $\delta$-Superderivations of simple finite-dimensional Jordan and Lie superalgebras. Algebra i logika, Tome 49 (2010) no. 2, pp. 195-215. http://geodesic.mathdoc.fr/item/AL_2010_49_2_a3/

[1] V. T. Filippov, “O $\delta$-differentsirovaniyakh algebr Li”, Sib. matem. zh., 39:6 (1998), 1409–1422 | MR | Zbl

[2] V. T. Filippov, “O $\delta$-differentsirovaniyakh pervichnykh algebr Li”, Sib. matem. zh., 40:1 (1999), 201–213 | MR | Zbl

[3] V. T. Filippov, “O $\delta$-differentsirovaniyakh pervichnykh alternativnykh i maltsevskikh algebr”, Algebra i logika, 39:5 (2000), 618–625 | MR | Zbl

[4] I. B. Kaigorodov, “O $\delta$-differentsirovaniyakh prostykh konechnomernykh iordanovykh superalgebr”, Algebra i logika, 46:5 (2007), 585–605 | MR | Zbl

[5] I. B. Kaigorodov, “O $\delta$-differentsirovaniyakh klassicheskikh superalgebr Li”, Sib. matem. zh., 50:3 (2009), 547–565 | MR

[6] V. G. Kac, “Lie superalgebras”, Adv. Math., 26:1 (1977), 8–96 | DOI | MR | Zbl

[7] I. Penkov, “Characters of strongly generic irreducible Lie superalgebra representations”, Int. J. Math., 9:3 (1998), 331–366 | DOI | MR | Zbl

[8] I. L. Kantor, “Iordanovy i lievy superalgebry, opredelennye algebroi Puassona”, Algebra i analiz, izd-vo TGU, Tomsk, 1989, 55–80 | MR

[9] V. G. Kac, “Classification of simple $Z$-graded Lie superalgebras and simple Jordan superalgebras”, Comm. Algebra, 5 (1977), 1375–1400 | DOI | MR | Zbl

[10] A. P. Pozhidaev, I. P. Shestakov, “Nekommutativnye iordanovy superalgebry stepeni $n>2$”, Algebra i logika, 49:1 (2010), 26–59 | MR

[11] K. A. Zhevlakov, A. M. Slinko, I. P. Shestakov, A. I. Shirshov, Koltsa, blizkie k assotsiativnym, Nauka, M., 1978 | MR | Zbl

[12] I. Kherstein, Nekommutativnye koltsa, Mir, M., 1972 | MR

[13] R. H. Oehmke, “On flexible algebras”, Ann. Math. (2), 68 (1958), 221–230 | DOI | MR | Zbl

[14] V. G. Skosyrskii, “Strogo pervichnye nekommutativnye iordanovy algebry”, Issledovaniya po teorii kolets i algebr, Tr. In-ta matem. SO AN SSSR, 16, Nauka, Novosibirsk, 1989, 131–163 | MR