Winter School JTP: Introduction to A-infinity structures, Bernhard Keller, Lecture 3

In this minicourse, we will present basic results on A-infinity algebras, their modules and their derived categories. We will start with two motivating problems from representation theory. Then we will briefly present the topological origin of A-infinity structures. We will then define and study A-infinity algebras and their morphisms. Of central importance are the bar construction and Kadeishvili’s theorem on the existence of minimal models. We will then define the derived category of an A-infinity algebra or category and describe its full subcategory generated by the representables using twisted objects.