r$_\infty$-Matrices, triangular L$_\infty$-bialgebras, and quantum$_\infty$ groups

Abstract

A homotopy analogue of the notion of a triangular Lie bialgebra is proposed with a goal of extending the basic notions of theory of quantum groups to the context of homotopy algebras and, in particular, introducing a homotopical generalization of the notion of a quantum group, or quantum$_\infty$-group.