Some graph theoretical characterizations of positive definite symmetric quasi-Cartan matrices

2014/12/03 by M. Abarca, D. Rivera, Abarca, M. +2
Mathematics · Physics and Astronomy · #05C75 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05C75

paper · pdf · doi:10.48550/arxiv.1412.1187

arxiv created 2014/12/03 · openalex publication_date 2014/12/03 · arxiv updated 2014/12/04 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We present some graphical characterizations of positive definite symmetric quasi-Cartan matrices of Dynkin type \mathbbA_n and \mathbbD_n. Our proofs are constructive, purely graph theoretical, and almost self-contained in the sense that they rely on the classical inflations method only.

Related

• Algorithms and Properties for Positive Symmetrizable Matrices
• Frises
• The Aizenbud-Lapid binary operation for symmetrizable Cartan types
• Positive definite matrices in the view-points of planar networks and cluster subalgebras
• The Classification of the Simply Laced Berger Graphs from Calabi-Yau CY₃ spaces