Formula omitted]-infinity structures related to bi-Koszul algebras

Abstract

Let A be a bi-Koszul algebra. We describe all possible A ∞ -algebra structures on the Ext-algebra E ( A ) and prove that E ( A ) must be [ m 2 , m 3 ] -finitely generated. We give an equivalent description of the condition for a connected graded algebra to be a bi-Koszul algebra in the language of A ∞ -algebras. We discuss decomposition in the case that E ( A ) is endowed with minimal number of multiplications.