For an associative commutative algebra A with Rota-Baxter operator R : A → A with weight λ denote by AR an algebra with linear space A and multiplication a ◦ b = aR(b). Let AR− and AR+ be the algebra AR under Lie and Jordan commutators. If λ = 0, then the algebra AR = (A, ◦) is Zinbiel, AR+ is associative, and AR− is Tortkara. We find polynomial identities of algebras AR, AR− and AR+ in the case λ ≠ 0. We prove that AR− is Tortkara. AR+ satisfies an identity of degree 5. In the case λ ≠ 0, the algebra AR is not associative-admissible.
This video is part of the Non-Associative Day in Online, run by the European Non-Associative Algebra Seminar series.
