Graphical characterization of positive definite non symmetric quasi-Cartan matrices

DOI10.1016/J.DISC.2018.01.013zbMath1397.05103OpenAlexW2792471144MaRDI QIDQ1709514

Claudia Pérez, Daniel E. Rivera

Publication date: 5 April 2018

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.disc.2018.01.013

zbMATH Keywords

equivalenceDynkin diagramassemblagenon-symmetric quasi-Cartan matrix

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Positive matrices and their generalizations; cones of matrices (15B48)

Related Items (12)

On algorithmic Coxeter spectral analysis of positive posets ⋮ Serre type relations for complex semisimple Lie algebras associated to positive definite quasi-Cartan matrices ⋮ Symbolic computation of strong Gram congruences for Cox-regular positive edge-bipartite graphs with loops ⋮ On polynomial time inflation algorithm for loop-free non-negative edge-bipartite graphs ⋮ Quadratic algorithm to compute the Dynkin type of a positive definite quasi-Cartan matrix ⋮ A Coxeter spectral classification of positive edge-bipartite graphs. II: Dynkin type \(\mathbb{D}_n\) ⋮ Coefficients of non-negative quasi-Cartan matrices, their symmetrizers and Gram matrices ⋮ Polynomial-time Classification of Skew-symmetrizable Matrices with a Positive Definite Quasi-Cartan Companion ⋮ On the structure of loop-free non-negative edge-bipartite graphs ⋮ Root systems and inflations of non-negative quasi-Cartan matrices ⋮ A computational technique in Coxeter spectral study of symmetrizable integer Cartan matrices ⋮ A Coxeter spectral classification of positive edge-bipartite graphs. I: Dynkin types \(\mathcal{B}_n\), \(\mathcal{C}_n\), \(\mathcal{F}_4\), \(\mathcal{G}_2\), \(\mathbb{E}_6\), \(\mathbb{E}_7\), \(\mathbb{E}_8\)

Cites Work

• Path-driven orientation of mixed graphs
• Generalized Serre relations for Lie algebras associated with positive unit forms
• On weakly positive unit forms
• A characterization of positive unit forms
• The Dynkin type of a non-negative unit form.
• Mesh Algorithms for Coxeter Spectral Classification of Cox-regular Edge-bipartite Graphs with Loops, II. Application to Coxeter Spectral Analysis
• Algorithms for Isotropy Groups of Cox-regular Edge-bipartite Graphs
• Introduction to the Representation Theory of Algebras
• Graph Theoretical and Algorithmic Characterizations of Positive Definite Symmetric Quasi-Cartan Matrices
• Cubic Algorithm to Compute the Dynkin Type of a Positive Definite Quasi-Cartan Matrix
• Symbolic Algorithms Computing Gram Congruences in the Coxeter Spectral Classification of Edge-bipartite Graphs, II. Isotropy Mini-groups
• Lie groups beyond an introduction
• A characterization of positive unit forms. II

This page was built for publication: Graphical characterization of positive definite non symmetric quasi-Cartan matrices