Cluster algebras with Grassmann variables

Q3 Mathematics

Electronic Research Announcements in Mathematical Sciences Pub Date : 2018-09-06 DOI:10.3934/ERA.2019.26.001

V. Ovsienko, M. Shapiro

引用次数: 21

Abstract

We develop a version of cluster algebra extending the ring of Laurent polynomials by adding Grassmann variables. These algebras can be described in terms of "extended quivers," which are oriented hypergraphs. We describe mutations of such objects and define a corresponding commutative superalgebra. Our construction includes the notion of weighted quivers that has already appeared in different contexts. This paper is a step towards understanding the notion of cluster superalgebra.

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具有Grassmann变量的簇代数

我们发展了一个版本的聚类代数，通过添加Grassmann变量来扩展Laurent多项式的环。这些代数可以用“扩展颤振”来描述，它们是定向超图。我们描述了这些对象的突变，并定义了相应的交换超代数。我们的结构包括加权颤振的概念，已经出现在不同的上下文中。本文是理解聚类超代数概念的一步。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Electronic Research Announcements in Mathematical Sciences 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Electronic Research Archive (ERA), formerly known as Electronic Research Announcements in Mathematical Sciences, rapidly publishes original and expository full-length articles of significant advances in all branches of mathematics. All articles should be designed to communicate their contents to a broad mathematical audience and must meet high standards for mathematical content and clarity. After review and acceptance, articles enter production for immediate publication. ERA is the continuation of Electronic Research Announcements of the AMS published by the American Mathematical Society, 1995—2007