On the $L_{\mathrm{\infty }}$-bialgebra structure of the rational homotopy groups ${\pi }_{\ast }(\mathrm{\Omega }\mathrm{\Sigma }Y)\otimes \mathbb{Q}$

We introduce the notion of an $L_{\mathrm{\infty }}$-bialgebra structure on a vector space. We show that the rational homotopy groups ${\pi }_{\ast }(\mathrm{\Omega }\mathrm{\Sigma }Y)\otimes \mathbb{Q}$ admit such a structure for the loop space $\mathrm{\Omega }\mathrm{\Sigma }Y$ of a suspension $\mathrm{\Sigma }Y$ that characterizes $Y$ up to rational homotopy equivalence.