Universal Constructions on Algebras over Operads

par Saikat Goswami (TCG Crest)

mardi 10 févr. 2026, 14:00 → 15:00 Europe/Paris

IMT 1R2 207 (Salle Pellos)

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.