论文标题
量子投影飞机在其中心有限
Quantum Projective Planes Finite over their Centers
论文作者
论文摘要
对于$ 3 $维的量子量子多项式代数$ a = \ Mathcal {a}（e，σ）$，artin-tate-van den bergh表明$ a $在其中心且仅在$ |σ|σ| <\ infty $时才有限。此外，Artin表明，如果$ a $在其中心上是有限的，而$ e \ neq \ mathbb {p}^2 $，则$ a $具有脂肪点模块，在非合并代数的几何形状中起着重要作用，但是总体上，匡威并非如此。在本文中，我们将证明，如果$ e \ neq \ neq \ neq \ mathbb {p}^2 $，则$ a $在且仅当量子射击平面$ \ mathsf {proj} _ {\ rm nc {\ rm nc} $ y if $ | $ | fifty $ | Nakayama $ a $。特别是在尤其是$ a $。我们将证明，如果$ e $的第二个hessian为零，则$ a $没有脂肪点模块。
For a $3$-dimensional quantum polynomial algebra $A=\mathcal{A}(E,σ)$, Artin-Tate-Van den Bergh showed that $A$ is finite over its center if and only if $|σ|<\infty$. Moreover, Artin showed that if $A$ is finite over its center and $E\neq \mathbb{P}^2$, then $A$ has a fat point module, which plays an important role in noncommutative algebraic geometry, however the converse is not true in general. In this paper, we will show that, if $E\neq \mathbb{P}^2$, then $A$ has a fat point module if and only if the quantum projective plane $\mathsf{Proj}_{\rm nc} A$ is finite over its center in the sense of this paper if and only if $|ν^*σ^3|<\infty$ where $ν$ is the Nakayama automorphism of $A$.In particular, we will show that if the second Hessian of $E$ is zero, then $A$ has no fat point module.
