(n+1)-Ary derivations of simple Malcev algebras
We defined (n+1)-ary derivations of n-ary algebras. We described 3-derivations of simple Malcev algebras and 4-ary derivations of simple ternary Malcev algebra M_8.
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arXiv subjects
Ivan Kaygorodov
Publications and source records attributed to Ivan Kaygorodov.
(n+1)-Ary derivations os semisimple Filippov algebras
We defined (n+1)-ary derivations of $n$-ary algebras. We described (n+1)-derivations of simple and semisimple finite-dimensional Filippov algebras over algebraically closed field zero characteristic. We constructed new examples of non-trivial (n+1)-ary derivations of Filippov algebras.
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Generalized δ-Derivations
We defined generalized δ-derivations of algebra A as linear mapping χassociated with usual δ-derivation ϕby the rule χ(xy)=δ(χ(x)y+xϕ(y))=δ(ϕ(x)y+xχ(y)) for any x,y \in A. We described generalized δ-derivations of prime alternative algebras, prime Lie algebras and superalgebras, unital algebras, and semisimple finite-dimensional Jordan superalgebras. In this cases we proved that generalized δ-derivation is a generalized derivation or δ-derivation. After that we described δ-superderivations of superalgebras < >, arising from prime alternative algebras, prime Lie algebras and superalgebras, unital algebras, and semisimple finite-dimensional Jordan superalgebras. In the end, we constructed new examples of non-trivial δ-derivations of Lie algebras.
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δ-derivations of n-ary algebras
We defined δ-derivations of n-ary algebras. We described δ-derivations of (n+1)-dimensional n-ary Filippov algebras and simple finite-dimensional Filippov algebras over algebraically closed field zero characteristic, and simple ternary Malcev algebra M_8. We constructed new examples of non-trivial δ-derivations of Filippov algebras and new examples of non-trivial antiderivations of simple Filippov algebras.
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$δ$-superderivations of KKM Double
We described $δ$-derivations and $δ$-superderivations of simple Jordan superalgebra < > (also known as superalgebra of Jordan brackets) and unital simple finite-dimensional Jordan superalgebras over algebraic closed fields with characteristic $p\neq2$. As a consequence, we received relationship between non-trivial $δ$-derivations and specialty of simple superalgebra < >. We constructed new examples of non-trivial 1/2-derivations of Jordan superalgebras of vector type.
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$δ$-superderivations of semisimple Jordan superalgebras
We described $δ$-derivations and $δ$-superderivations of simple and semisimple finite-dimensional Jordan superalgebras over algebraic closed fields with characteristic $p\neq2$. We constructed new examples of 1/2-derivations and 1/2-superderivations of simple Zelmanov's superalgebra $V_{1/2}(Z,D).$
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Generalized Kantor Double
We consider generalization of wellknown construction Kantor Double J(Γ, {,}) (KKM Double, Kantor-King-McCrimmon Double), where basic algebra Γ is nonunital algebra. We find necessary and sufficient conditions for a generalized Kantor double to be Jordan. We also describe $δ$-superderivations of a generalized Kantor double whose even part is prime.
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$δ$-derivations of classical Lie superalgebras
We consider the $δ$-derivations of classical Lie superalgebras and prove that these superalgebras admit nonzero $δ$-derivations only when $δ= 0,1/2,1$. The structure of $1/2$-derivations for classical Lie superalgebras is completely determined.
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$δ$-derivations of simple Jordan algebras and superalgebras
We describe non-trivial $δ$-derivations of semisimple finite-dimensional Jordan algebras over an algebraically closed field of characteristic not 2, and of simple finite-dimensional Jordan superalgebras over an algebraically closed field of characteristic 0. For these classes of algebras and superalgebras, non-zero $δ$-derivations are shown to be missing for $δ\neq 0,{1}{2},1$, and we give a complete account of ${1}{2}$-derivations.
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$δ$-superderivations of simple finite-dimensional Jordan and Lie superalgebras
We introduce the concept of a $δ$-superderivation of a superalgebra. $δ$-Derivations of Cartan-type Lie superalgebras are treated, as well as $δ$-superderivations of simple finite-dimensional Lie superalgebras and Jordan superalgebras over an algebraically closed field of characteristic 0. We give a complete description of $\{1}{2}$-derivations for Cartan-type Lie superalgebras. It is proved that nontrivial $δ$-(super)derivations are missing on the given classes of superalgebras, and as a consequence, $δ$-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 $δ$-derivations of unital flexible and semisimple finite-dimensional Jordan algebras over a field of characteristic not 2.
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