Abstract: We describe all homogeneous structures of ternary Leibniz algebras on a free dialgebra. As a corollary, we find the structure of a Lie triple system on an arbitrary dialgebra and a conformal associative algebra. We also describe all homogeneous structures of an (epsilon, delta)-Freudenthal-Kantor triple system on a dialgebra. We find some homogeneous structures of Rota-Baxter algebras arising on a 0-dialgebra with an associative bar-unity. As a corollary, the structure of a Rota-Baxter algebra on an arbitrary associative dialgebra with a bar-unity and a conformal associative algebra is given. We prove that an arbitrary alternative dialgebra may be embedded into an alternative dialgebra with a bar-unity. We introduce a notion of the variety of dialgebras in the sense of Eilenberg, which is equivalent to one introduced by P. S. Kolesnikov.

Cite: Pozhidaev A.P.
0-Dialgebras with bar-unity, Rota-Baxter and 3-Leibniz algebras
In compilation GROUPS, RINGS AND GROUP RINGS. 2009. – Т.499. – C.245-256. WOS

Identifiers:

Web of science:

WOS:000276433100021

Citing:

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