论文标题
简单志趣相投的群集类别四边形
Negative cluster categories from simple minded collection quadruples
论文作者
论文摘要
Fomin和Zelevinsky对群集代数的定义奠定了集群理论的基础。原始定义的各种分类和概括导致Iyama和Yoshino的广义聚类类别$ \ Mathcal {T}/\ Mathcal {T}^{fd} $来自阳性calabi-yau triples $（\ Mathcal {t} t}，\ Mathcal {金后来定义了简单的思想集合四元素$（\ nathcal {t}，\ Mathcal {t}^{p}，\ Mathbb {s}，\ Mathcal {s}）$三元组。 在本文中，我们进一步研究商类别$ \ MATHCAL {T}/\ MATHCAL {t}^p $来自简单志趣相投的Quadruples。我们的主要结果使用限制和colimits来描述$ \ Mathcal {t}/\ Mathcal {t}^p $上的HOM空间，这与更易于理解$ \ Mathcal {t} $的HOM空间有关。此外，我们将定理应用于JIN的结果：如果我们有负面的-Calabi-yau三倍，则$ \ Mathcal {t}/\ Mathcal {T}^p $是负群集类别。
Fomin and Zelevinsky's definition of cluster algebras laid the foundation for cluster theory. The various categorifications and generalisations of the original definition led to Iyama and Yoshino's generalised cluster categories $\mathcal{T}/\mathcal{T}^{fd}$ coming from positive-Calabi-Yau triples $(\mathcal{T}, \mathcal{T}^{fd},\mathcal{M})$. Jin later defined simple minded collection quadruples $(\mathcal{T}, \mathcal{T}^{p},\mathbb{S},\mathcal{S})$, where the special case $\mathbb{S}=Σ^{-d}$ is the analogue of Iyama and Yang's triples: negative-Calabi-Yau triples. In this paper, we further study the quotient categories $\mathcal{T}/\mathcal{T}^p$ coming from simple minded collection quadruples. Our main result uses limits and colimits to describe Hom-spaces over $\mathcal{T}/\mathcal{T}^p$ in relation to the easier to understand Hom-spaces over $\mathcal{T}$. Moreover, we apply our theorem to give a different proof of a result by Jin: if we have a negative-Calabi-Yau triple, then $\mathcal{T}/\mathcal{T}^p$ is a negative cluster category.
