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Register a new user$n$-ary algebras of the first level
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Authors
Yury Volkov
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No Arabic abstract
$n$-ary algebras of the first degeneration level are described. A detailed classification is given in the cases $n=2,3$.
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In this paper, we define $omega$-derivations, and study some properties of $omega$-derivations, with its properties we can structure a new $n$-ary Hom-Nambu algebra from an $n$-ary Hom-Nambu algebra. In addition, we also give derivations and representations of $n$-ary Hom-Nambu algebras.
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 that admits pure local derivations, i.e. algebra admits a local derivation which is not a derivation.
We present $PL_{infty}$-algebras in the form of composition of maps and show that a $PL_{infty}$-algebra $V$ can be described by a nilpotent coderivation on coalgebra $P^*V$ of degree $-1$. Using coalgebra maps among $T^*V$, $wedge^*V$, $P^*V$, we show that every $A_{infty}$-algebra carries a $PL_{infty}$-algebra structure and every $PL_{infty}$-algebra carries an $L_{infty}$-algebra structure. In particular, we obtain a pre Lie $n$-algebra structure on an arbitrary partially associative $n$-algebra and deduce pre Lie $n$-algebras are $n$-Lie admissible.
In the present paper we obtain the list of algebras, up to isomorphism, such that closure of any complex finite-dimensional algebra contains one of the algebra of the given list.
This paper is devoted to the description of complex finite-dimensional algebras of level two. We obtain the classification of algebras of level two in the varieties of Jordan, Lie and associative algebras.
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