# A categorical characterization of quantum projective spaces

### Izuru Mori

Shizuoka University, Japan### Kenta Ueyama

Hirosaki University, Japan

## Abstract

Let $R$ be a finite dimensional algebra of finite global dimension over a field $k$. In this paper, we will characterize a $k$-linear abelian category $\mathscr C$ such that $\mathscr C\cong \operatorname {tails} A$ for some graded right coherent AS-regular algebra $A$ over $R$. As an application, we will prove that if $\mathscr C$ is a smooth quadric surface in a quantum $\mathbb P^3$ in the sense of Smith and Van den Bergh, then there exists a right noetherian AS-regular algebra $A$ over $kK_2$ of dimension 3 and of Gorenstein parameter 2 such that $\mathscr C\cong \operatorname {tails} A$ where $kK_2$ is the path algebra of the 2-Kronecker quiver $K_2$.

## Cite this article

Izuru Mori, Kenta Ueyama, A categorical characterization of quantum projective spaces. J. Noncommut. Geom. 15 (2021), no. 2, pp. 489–529

DOI 10.4171/JNCG/403