映射类群的表述及其在曲面簇代数中的应用

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra Pub Date : 2024-10-11 DOI:10.1016/j.jalgebra.2024.09.014

Jinlei Dong, Fang Li

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引用次数: 0

摘要

在本文中，我们介绍了任意种属的稳定边界的标记曲面的映射类群。需要注意的是，在已有的著作中，标注曲面的映射类群是同次同构的同位类，它们点对点地固定边界。作为稳定边界的标注曲面的映射类群的呈现的应用，我们从可行曲面（S,M）得到了簇代数的簇自形群的呈现。最后，对于（1）4-穿孔球面的情况，从曲面得到了簇代数的簇自形群的特征。由于在[1]中给出了来自这些曲面的簇代数的簇自形群在(2)一次穿孔的 4 球面和(3)两次穿孔的 digon 面中的情况，我们实际上给出了来自不可行曲面的簇代数的簇自形群。

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Presentations of mapping class groups and an application to cluster algebras from surfaces

In this paper, we give presentations of the mapping class groups of marked surfaces stabilizing boundaries for any genus. Note that in the existing works, the mapping class groups of marked surfaces were the isotopy classes of homeomorphisms fixing boundaries pointwise. The condition for stabilizing boundaries of mapping class groups makes the requirement for mapping class groups to fix boundaries pointwise to be unnecessary.

As an application of presentations of the mapping class groups of marked surfaces stabilizing boundaries, we obtain the presentation of the cluster automorphism group of a cluster algebra from a feasible surface

(S, M)

Lastly, for the case (1) 4-punctured sphere, the cluster automorphism group of a cluster algebra from the surface is characterized. Since cluster automorphism groups of cluster algebras from those surfaces were given in [1] in the cases (2) the once-punctured 4-gon and (3) the twice-punctured digon, we indeed give presentations of cluster automorphism groups of cluster algebras from surfaces which are not feasible.

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来源期刊

Journal of Algebra 数学-数学

CiteScore

1.50

自引率

22.20%

发文量

414

审稿时长

2-4 weeks

期刊介绍： The Journal of Algebra is a leading international journal and publishes papers that demonstrate high quality research results in algebra and related computational aspects. Only the very best and most interesting papers are to be considered for publication in the journal. With this in mind, it is important that the contribution offer a substantial result that will have a lasting effect upon the field. The journal also seeks work that presents innovative techniques that offer promising results for future research.