A-infinity Bialgebras of Type (m,n)

TL;DR

This paper introduces A-infinity bialgebras of type (m,n), detailing their structure relations and providing algebraic examples for various parameters, expanding the understanding of these algebraic structures.

Contribution

It characterizes the structure relations for A-infinity bialgebras of type (m,n) and constructs explicit algebraic examples for all relevant parameters.

Findings

Derived the structure relations for A-infinity bialgebras of type (m,n)

Constructed algebraic examples for each m ≥ 2 and m+n ≥ 4

Extended the theory of A-infinity bialgebras with explicit models

Abstract

An A-infinity bialgebra of type (m,n) is a Hopf algebra H equipped with a "compatible" operation \omega : H^{\otimes m} \to H^{\otimes n} of positive degree. We determine the structure relations for A-infinity bialgebras of type (m,n) and construct a purely algebraic example for each m \geq 2 and m+n \geq 4.