Cluster Algebras and Semi-invariant Rings II. Projections

2015/08/23 by Jiarui Fei, Fei, Jiarui
Mathematics · #16G20 #52B20 #Commutative Algebra (math.AC) #FOS: Mathematics #Primary 13F60 #Representation Theory (math.RT) #Rings and Algebras (math.RA) #Secondary 13A50 #math.AC #math.RA #math.RT #msc:13A50 #msc:13F60 #msc:16G20 #msc:52B20

paper · pdf · doi:10.48550/arxiv.1508.05563

28 pages, 5 figures. text overlap with arXiv:1504.02970, arXiv:1411.4693. v2. fix typos, and add one conjecture

arxiv created 2015/08/30 · arxiv updated 2015/09/01

Abstract

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

Citations

• Cluster Algebras, Invariant Theory, and Kronecker Coefficients I

Cited by

• Cluster Algebras, Invariant Theory, and Kronecker Coefficients I

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