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Jordan algebras admitting derivations with invertible values
Ivan Kaygorodov, Artem Lopatin, Yury Popov
The notion of derivation with invertible values as a derivation of ring with unity that only takes multiplicatively invertible or zero values appeared in a paper of Bergen, Herstei…
Algebras of Jordan brackets and Generalized Poisson algebras
Ivan Kaygorodov
We construct a basis of free unital generalized Poisson superalgebras and a basis of free unital superalgebras of Jordan brackets. Also, we prove the analogue of Farkas' Theorem fo…
Conservative algebras of -dimensional algebras, II
Ivan Kaygorodov, Yury Volkov
In 1990 Kantor defined the conservative algebra of all algebras (i.e. bilinear maps) on the -dimensional vector space. If , then the algebra does not belong t…
Generalized derivations of (color) n-ary algebras
Ivan Kaygorodov, Yury Popov
We generalize the results of Leger and Luks about generalized derivations of Lie algebras to the case of color -ary -algebras. Particularly, we prove some properties of gener…
On The Kantor Product
Ivan Kaygorodov
We study the algebra of bilinear multiplications of an -dimensional vector space. In particular, we study the Kantor product of some well-known (associative, Lie, alternative, N…
A characterization of nilpotent nonassociative algebras by invertible Leibniz-derivations
Ivan Kaygorodov, Yury Popov
Moens proved that a finite-dimensional Lie algebra over field of characteristic zero is nilpotent if and only if it has an invertible Leibniz-derivation. In this article we prove t…