Universal Constructions on Algebras over Operads

Abstract: We construct a universal coacting bialgebra and Hopf algebra for any finite-dimensional algebra over a symmetric operad. This work extends previous constructions of Agore and Militaru to the operadic setting. We show that the category of finite-dimensional algebras over operads is enriched over the dual of commutative algebras, which induces a canonical bialgebra structure on the associated universal coacting algebra. Our framework recovers known constructions for Lie, Leibniz, and Poisson algebras, offering a unified operadic perspective on coacting objects across a broad class of algebras.

quantum algebrarings and algebras

Audience: researchers in the topic

European Non-Associative Algebra Seminar