Hopf structures on the multiplihedra

TL;DR

This paper explores algebraic structures on the vertices of multiplihedra, focusing on two Hopf module structures over the Loday-Ronco Hopf algebra, relevant to higher categories and homotopy theory.

Contribution

It introduces two novel Hopf module structures on the multiplihedra vertices, expanding the algebraic understanding of these polytopes.

Findings

Identification of two distinct Hopf module structures

Connection to higher categories and homotopy theory

Extension of algebraic frameworks for multiplihedra

Abstract

We investigate algebraic structures that can be placed on vertices of the multiplihedra, a family of polytopes originating in the study of higher categories and homotopy theory. Most compelling among these are two distinct structures of a Hopf module over the Loday-Ronco Hopf algebra.