Work

Categorifications of Non-Integer Quivers: Types 𝐻₄, 𝐻₃ and 𝐼₂(2𝑛+1)

Year: 2024

Type: article

Abstract: We define the notion of a weighted unfolding of quivers with real weights, and use this to provide a categorification of mutations of quivers of finite types H 4 H_4 , H 3 H_3 and I 2 ( 2 n + 1 ) I_2(2n+1) . In particular, the (un)folding induces a semiring action on the categories associated to the unfolded quivers of types E 8 E_8 , D 6 D_6 and A 2 n A_{2n} respectively. We then define the tropical seed pattern on the folded quivers, which includes c c - and g g -vectors, and show its compatibility with the unfolding.

Source: Representation Theory of the American Mathematical Society

DOI: 10.1090/ert/671

Authors: Drew Duffield, Pavel Tumarkin

Institution: Durham University

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Leverhulme Trust, Engineering and Physical Sciences Research Council, Division of Mathematical Sciences

Awards: G3081709163, G3691759950, Isaac Newton Institute for Mathematical Sciences, G5831833421, G8892464670