On $\ddot{I}„$-tilting theory

Abstract

We give a brief introduction to $\ddot{I}„$-tilting theory [AIR]. In particular, we will see how our theory unifies two different branches of tilting theory, namely, silting theory and cluster tilting theory. We also introduce the history and recent developments.

This is a short summary of our Frontiers of Science Award paper "$\ddot{I}„$-tilting theory'' (Compos. Math. 2014)