JournalsjncgVol. 15, No. 2pp. 489–529

A categorical characterization of quantum projective spaces

  • Izuru Mori

    Shizuoka University, Japan
  • Kenta Ueyama

    Hirosaki University, Japan
A categorical characterization of quantum projective spaces cover
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Abstract

Let RR be a finite dimensional algebra of finite global dimension over a field kk. In this paper, we will characterize a kk-linear abelian category C\mathscr C such that CtailsA\mathscr C\cong \operatorname {tails} A for some graded right coherent AS-regular algebra AA over RR. As an application, we will prove that if C\mathscr C is a smooth quadric surface in a quantum P3\mathbb P^3 in the sense of Smith and Van den Bergh, then there exists a right noetherian AS-regular algebra AA over kK2kK_2 of dimension 3 and of Gorenstein parameter 2 such that CtailsA\mathscr C\cong \operatorname {tails} A where kK2kK_2 is the path algebra of the 2-Kronecker quiver K2K_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