Cluster algebras and semi-invariant rings II: projections

被引：5

作者：

Fei, Jiarui ^{[1
]}

机构：

[1] Natl Ctr Theoret Sci, Taipei 10617, Taiwan

来源：

MATHEMATISCHE ZEITSCHRIFT | 2017年 / 285卷 / 3-4期

关键词：

Cluster algebra; Semi-invariant ring; Quiver representation; Graded upper cluster algebra; Quiver with potential; Weight restriction; Orthogonal projection; Vertex removal; Exceptional sequence; Cluster character; Polytope; Lattice point; QUIVERS; REPRESENTATIONS; COEFFICIENTS; POTENTIALS; SATURATION; MODULI;

D O I：

10.1007/s00209-016-1733-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let SI beta(Q) be the semi-invariant ring of beta-dimensional representations of a quiver Q. Suppose that (Q, beta) projects to another quiver with dimension vector (Q', beta') through an exceptional representation E. We show that if SI beta(Q) is the upper cluster algebra associated to an ice quiver Delta, then SI beta' (Q') is the upper cluster algebra associated to Delta' , where Delta' is obtained from Delta through simple operations depending on E. We also study the relation of their bases using the quiver with potential model.

引用

页码：939 / 966

页数：28

共 29 条

[1]

[Anonymous], 1972, INTRO LIE ALGEBRAS R

[2]

Atiyah M. F., 1969, Introduction to Commutative Algebra

[3] Cluster algebras III: Upper bounds and double Bruhat cells [J].