Defects in Spin Chains via Cluster Categories
Ammar Husain
TL;DR
This paper explores the algebraic structures of cluster categories related to spin chains, focusing on Picard and K_0 groups, and discusses their deformation quantizations, shedding light on boundaries and defects in quantum spin systems.
Contribution
It introduces a novel analysis of Picard and K_0 groups for cluster algebras from cluster categories, linking algebraic properties to physical boundary and defect phenomena in spin chains.
Findings
Characterization of Picard groups for cluster algebras
Analysis of K_0 groups in the context of cluster categories
Discussion on deformation quantizations of these structures
Abstract
We study Picard groups and groups for the cluster algebras that come from the cluster categories of \cite{HernandezLeclerc}. This is inspired by a study of boundaries and defects in the associated spin chains. We also do some discussion for their formal deformation quantizations.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology