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arXiv · 1708.00167

A categorical characterization of quantum projective spaces

Izuru Mori·Kenta Ueyama
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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.

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Izuru Mori, Kenta Ueyama. 2017-08-01. A categorical characterization of quantum projective spaces. https://arxiv.org/abs/1708.00167

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