A-infinity structures related to bi-Koszul algebras

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.

20 pages