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A Graph Theoretical Framework for the Strong Gram Classification of Non-negative Unit Forms of Dynkin Type 𝔸 n

González Jiménez, Arturo Jesús

Fundamenta Informaticae

2021

Vol. 184, nr 1

49--82

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 An . 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 An . With these tools, connected principal unit forms of Dynkin type An are also classified up to strong congruence.