A-infinity structures related to bi-Koszul algebras

TL;DR

This paper characterizes all $A__$-algebra structures on the Ext-algebra of bi-Koszul algebras, showing they are finitely generated by specific multiplications, and provides an $A__$-theoretic characterization of bi-Koszulity.

Contribution

It offers a complete description of $A__$-structures on Ext-algebras of bi-Koszul algebras and characterizes bi-Koszulity via $A__$-language.

Findings

$E(A)$ must be $[m_2, m_3]$-finitely generated

Connected graded algebra is bi-Koszul iff described by $A__$-structure

Minimal multiplications case analyzed for decomposition

Abstract

Let $A$ be a bi-Koszul algebra, we describe all possible $A_\infty$-algebra structures on the Ext-algebra $E(A)$, and prove that $E(A)$ must be $[m_2, m_3]$-finitely generated. An equivalent description for a connected graded algebra to be a bi-Koszul algebra is given in terms of $A_\infty$-language. The case that $E(A)$ is endowed with minimal number of multiplications is discussed for decomposition.