From entangled codipterous coalgebras to coassociative manifolds

TL;DR

This paper introduces a novel framework connecting coassociative coalgebras with advanced algebraic structures and explores the concept of coassociative manifolds, expanding the mathematical landscape.

Contribution

It constructs new algebraic objects from coassociative coalgebras and introduces the idea of coassociative manifolds, bridging different algebraic theories.

Findings

Construction of Poisson and Leibniz algebras from coalgebras

Introduction of coassociative manifolds concept

Expansion of algebraic structures derived from coalgebras

Abstract

We construct from coassociative coalgebras, bialgebras, Hopf algebras, new objects such as Poisson algebras, Leibniz algebras defined by J-L Loday and M. Ronco and explore the notion of coassociative manifolds.