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. 
@article{AL_2010_49_2_a3,
     author = {I. B. Kaigorodov},
     title = {$\delta${-Superderivations} of simple finite-dimensional {Jordan} and {Lie} superalgebras},
     journal = {Algebra i logika},
     pages = {195--215},
     publisher = {mathdoc},
     volume = {49},
     number = {2},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2010_49_2_a3/}
}
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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/