Multiplier Infinitesimal Bialgebras and Derivator Lie Bialgebras

TL;DR

This paper introduces the concepts of multiplier infinitesimal bialgebras and derivator Lie bialgebras, providing foundational definitions, examples, and establishing a connection between these structures.

Contribution

It defines new algebraic structures and demonstrates how multiplier infinitesimal bialgebras relate to multiplier Lie bialgebras, advancing the theoretical framework.

Findings

Defined multiplier infinitesimal bialgebras and derivator Lie bialgebras

Provided examples of these structures

Proved that bibalanced multiplier infinitesimal bialgebras induce multiplier Lie bialgebras

Abstract

We propose a definition of multiplier infinitesimal bialgebra and a definition of derivator Lie bialgebra. We give some examples of these structures and prove that every bibalanced multiplier infinitesimal bialgebra gives rise to a multiplier Lie bialgebra.