Let $\mathcal{ C}$ be an additive category equipped with an automorphism $\Sigma$. We show how to obtain $n$-angulations of $(\mathcal{ C},\Sigma)$ using some particular periodic injective resolutions. We give necessary and sufficient conditions on $(\mathcal{ C},\Sigma)$ admitting an $n$-angulation. Then we apply these characterizations to explain the standard construction of $n$-angulated categories and the $n$-angulated categories arising from some local rings. Moreover, we obtain a class of new examples of $n$-angulated categories from quasi-periodic selfinjective algebras.
Categories: math.RT math.RA