A categorical characterization of quantum projective spaces
Izuru Mori, Kenta Ueyama · Journal of Noncommutative Geometry · 2021
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 .