A graph theoretical framework for the strong Gram classification of non-negative unit forms of Dynkin type A
Year: 2021
Type: article
Abstract: In the context of signed line graphs, this article introduces a modified inflation technique to study strong Gram congruence of non-negative (integral quadratic) unit forms, and uses it to show that weak and strong Gram congruence coincide among positive unit forms of Dynkin type A. The concept of inverse of a quiver is also introduced, and is used to obtain and analyze the Coxeter matrix of non-negative unit forms of Dynkin type A. Connected principal unit forms of such type are also classified. Comment: Integral quadratic form, Gram congruence, quiver, Dynkin type, Coxeter matrix, edge-bipartite graph, signed line graph
Source: Fundamenta Informaticae
DOI: 10.46298/fi.7596
Author: Jesus Arturo Jimenez Gonzalez
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $4,150
OpenAlex ID: W7214728720