Let be a finite dimensional algebra of finite global dimension over a field . In this paper, we will characterize a -linear abelian category such that for some graded right coherent AS-regular algebra over . As an application, we will prove that if is a smooth quadric surface in a quantum in the sense of Smith and Van den Bergh, then there exists a right noetherian AS-regular algebra over of dimension 3 and of Gorenstein parameter 2 such that where is the path algebra of the 2-Kronecker quiver .
Cite this article
Izuru Mori, Kenta Ueyama, A categorical characterization of quantum projective spaces. J. Noncommut. Geom. 15 (2021), no. 2, pp. 489–529DOI 10.4171/JNCG/403