Δ-Derivations OF SEMISIMPLE FINITE-DIMENSIONAL STRUCTURABLE ALGEBRAS

Abstract

In this paper, we show the absence of nontrivial δ-derivations of semisimple finitedimensional structurable algebras over an algebraically closed field of characteristic not equal to 2, 3, 5.

Conservative algebras of 2-dimensional algebras

“…Since −D(ξ 2 ) = D(ξ 2 )ξ 1 + ξ 2 D(ξ 1 ), we obtain α 14 = α 24 = α 25 = α 26 = 0, α 23 = 2α 12 . Noted, that left multiplications on elements ξ 2 and ξ 5 are derivations ad ξ2 and ad ξ5 .…”

“…Recently a great interest has been shown to the study of Jordan and Lie algebras and superalgebras, as well as their generalizations with derivations. Namely, Popov determined the structure of differentiably simple Jordan algebras [8]; Kaygorodov and Popov described the structure of Jordan algebras with derivations with invertible values [9] and the structure of Jordan algebras with invertible Leibniz-derivations [10]; Barreiro, Elduque and Martínez descibed derivations of Cheng-Kac Jordan superalgebra [11]; Kaygorodov and Okhapkina found all δ-derivations of semisimple structurable algebras [12]; Kaygorodov, Shestakov, Zhelyabin and Zusmanovich studied generalized derivations of Jordan and Lie algebras and superalgebras in [13]- [20].…”

Generalized Derivations of n-BiHom-Lie algebras

“…n-ary Hom-type generalization of n-ary algebras were introduced in [2]. Derivations and generalized derivations of many varieties of algebras and Hom-algebras were investigated in [5,11,12,13,14,16,17,18,19,20,21,22,24,25,4,31,32,33,34].…”

О $(n+1)$-арных дифференцированиях полупростых алгебр Филиппова

“…В свое время -дифференцирования изучались в работах [1]- [14], где были описаны -дифференцирования первичных лиевых алгебр [1], [2], первичных альтернативных и мальцевских алгебр [3], простых и первичных лиевых супералгебр [6], [7], [4], полу-простых конечномерных йордановых алгебр и супералгебр [5], [7], [8], [10], полупро-стых структуризуемых алгебр [13], алгебр Филиппова малых размерностей и про-стых конечномерных алгебр Филиппова [11], а также простой тернарной алгебры Мальцева 8 [11]. В частности, были построены примеры нетривиальных -диффе-ренцирований для некоторых алгебр Ли [2], [4], [12], простых йордановых суперал-гебр [8], [10] и -арных алгебр Филиппова размерности + 1 (см.…”