论文标题
加权表面代数的虚拟突变
Virtual mutations of weighted surface algebras
论文作者
论文摘要
基于群集代数理论激发的表面三角剖分，在代数封闭场上的有限维对称代数已得到广泛研究和应用。特别是，在[16] - [20]中引入并研究了加权表面代数及其变形，并且显示出所有这些代数（除少数单数奇数外）都是对称的驯服定期代数，为$ 4 $。在本文中，使用[19]的加权表面代数的一般形式，我们介绍和研究称为加权表面代数的虚拟突变，该突变构成了新的大型对称的对称的驯服定期定期，$ 4 $。我们证明所有这些代数都是等效的，但不是同构与加权表面代数的同构。我们将此类代数与任何三角形的表面相关联，首先将边缘家族的爆炸与$ 2 $ - 三角盘，然后将其加权表面代数的虚拟突变进行。本文的结果构成了所有驯服对称周期性代数的分类的重要步骤。
The finite-dimensional symmetric algebras over an algebraically closed field, based on surface triangulations, motivated by the theory of cluster algebras, have been extensively investigated and applied. In particular, the weighted surface algebras and their deformations were introduced and studied in [16]-[20], and it was shown that all these algebras, except few singular cases, are symmetric tame periodic algebras of period $4$. In this article, using the general form of a weighted surface algebra from [19], we introduce and study so called virtual mutations of weighted surface algebras, which constitute a new large class of symmetric tame periodic algebras of period $4$. We prove that all these algebras are derived equivalent but not isomorphic to weighted surface algebras. We associate such algebras to any triangulated surface, first taking blow-ups of a family of edges to $2$-triangle discs, and then virtual mutations of their weighted surface algebras. The results of this paper form an essential step towards a classification of all tame symmetric periodic algebras.
