In the present paper we prove that every local and 2-local derivation of the complex finite dimensional simple Filippov algebra is a derivation. As a corollary we have the description of all local ...and 2-local derivations of complex finite dimensional semisimple Filippov algebras. All local derivations of the ternary Malcev algebra
M
8
are described. It is the first example of a finite-dimensional simple algebra which admits pure local derivations, i.e. algebra admits a local derivation which is not a derivation.
We give a geometric classification of complex
n
-dimensional 2-step nilpotent (all, commutative and anticommutative) algebras. Namely, it has been found the number of irreducible components and their ...dimensions. As a corollary, we have a geometric classification of complex 5-dimensional nilpotent associative algebras. In particular, it has been proven that this variety has 11 irreducible components and 7 rigid algebras.
12-derivations of Lie algebras and transposed Poisson algebras Ferreira, Bruno Leonardo Macedo; Kaygorodov, Ivan; Lopatkin, Viktor
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas,
2021/7, Volume:
115, Issue:
3
Journal Article
Peer reviewed
A relation between
1
2
-derivations of Lie algebras and transposed Poisson algebras has been established. Some non-trivial transposed Poisson algebras with a certain Lie algebra (Witt algebra, the ...algebra
W
(
a
,
-
1
)
, the thin Lie algebra and a solvable Lie algebra with abelian nilpotent radical) have been done. In particular, we have developed an example of the transposed Poisson algebra with associative and Lie parts isomorphic to the Laurent polynomials and the Witt algebra. On the other side, it has been proved that there are no non-trivial transposed Poisson algebras with a Lie algebra part isomorphic to a semisimple finite-dimensional algebra, a simple finite-dimensional superalgebra, the Virasoro algebra,
N
=
1
and
N
=
2
superconformal algebras, or a semisimple finite-dimensional
n
-Lie algebra.
The algebraic and geometric classification of all complex 3-dimensional transposed Poisson algebras is obtained. Also we discuss special 3-dimensional transposed Poisson algebras.
This paper is devoted to the complete algebraic and geometric classification of complex 5-dimensional nilpotent binary Leibniz and 4-dimensional nilpotent mono Leibniz algebras. As a corollary, we ...have the complete algebraic and geometric classification of complex 4-dimensional nilpotent algebras of nil-index 3.
This paper is devoted to the complete algebraic and geometric classification of complex four and five-dimensional antiassociative algebras. In particular, we proved that the variety of complex ...four-dimensional antiassociative algebras has dimension 12 and it is defined by three irreducible components (in particular, there is only 1 rigid algebra in this variety); the variety of complex five-dimensional antiassociative algebras has dimension 24 and it is defined by 8 irreducible components (in particular, there are only 4 rigid algebras in this variety).
We describe all central extensions of all 3-dimensional nontrivial complex Zinbiel algebras. As a corollary, we have a full classification of 4-dimensional nontrivial complex Zinbiel algebras and a ...full classification of 5-dimensional nontrivial complex Zinbiel algebras with 2-dimensional annihilator, which gives the principal step in the algebraic classification of 5-dimensional Zinbiel algebras.
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