Abstract Let $\mathscr{C}$ be a $(d+2)$ -angulated category with d -suspension functor $\Sigma^d$ . Our main results show that every Serre on is functor. We also has $\mathbb{S}$ if and only Auslander–Reiten -angles. Moreover, $\tau_d=\mathbb{S}\Sigma^{-d}$ where $\tau_d$ -Auslander–Reiten translation. These generalize work by Bondal–Kapranov Reiten–Van den Bergh. As an application, we prove fo...

these are notes from introductory survey lectures given at the institute for studies in theoretical physics and mathematics (ipm), teheran, in 2008 and 2010. we present the definition and the fundamental properties of fomin-zelevinsky’s cluster algebras. then, we introduce quiver representations and show how they can be used to construct cluster variables, which are the canonical generators of ...