On antisymmetric infinitesimal conformal bialgebras

[摘要] In this paper, we construct a bialgebra theory for associative conformal algebras, namely antisymmetric infinitesimal conformal bialgebras. On the one hand, it is an attempt to give conformal structures for antisymmetric infinitesimal bialgebras. On the other hand, under certain conditions, such structures are equivalent to double constructions of Frobenius conformal algebras, which are associative conformal algebras that are decomposed into the direct sum of another associative conformal algebra and its conformal dual as C[partial derivative]-modules such that both of them are subalgebras and the natural conformal bilinear form is invariant. The coboundary case leads to the introduction of associative conformal Yang-Baxter equation whose antisymmetric solutions give antisymmetric infinitesimal conformal bialgebras. Moreover, the construction of antisymmetric solutions of associative conformal Yang-Baxter equation is given from O-operators of associative conformal algebras as well as dendriform conformal algebras. (C) 2021 Elsevier Inc. All rights reserved.

[发布日期] 2021-11-15

[关键词] Associative conformal algebra;Dendriform conformal algebra;Associative conformal Yang-Baxter equation;O-operator;Rota-Baxter operator