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0-dialgebras with bar-unity and nonassociative Rota–Baxter algebras. (Russian, English) Zbl 1224.17003
Sib. Mat. Zh. 50, No. 6, 1356-1369 (2009); translation in Sib. Math. J. 50, No. 6, 1070-1080 (2009).
Summary: We describe all homogeneous structures of Rota–Baxter algebras on a 0-dialgebra with associative bar-unity and give a corollary on the structure of a Rota–Baxter algebra on an arbitrary associative dialgebra with bar-unity as well as a unital associative conformal algebra. We prove that an arbitrary alternative dialgebra may be embedded into an alternative dialgebra with associative barunity. We suggest the definition of variety of dialgebras in the sense of Eilenberg which is equivalent to that introduced earlier by P. S. Kolesnikov in [Sib. Math. J. 49, No. 2, 257-272 (2008; Zbl 1164.17002)].

MSC:
17A32 Leibniz algebras
17A20 Flexible algebras
17A30 Nonassociative algebras satisfying other identities
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