Frobenius-Perron theory of representation-directed algebras
J. M. Chen, J. Y. Chen
TL;DR
This paper investigates the Frobenius-Perron dimension in representation-directed algebras and canonical algebras of type ADE, establishing that these dimensions are always zero or one under certain conditions.
Contribution
It proves that the Frobenius-Perron dimension of a representation-directed algebra is always zero and characterizes when quotient algebras of canonical algebras have Frobenius-Perron dimension zero.
Findings
Frobenius-Perron dimension of a representation-directed algebra is always zero.
Frobenius-Perron dimension of quotient algebras of canonical algebras of type ADE is 0 or 1.
Provides necessary and sufficient conditions for Frobenius-Perron dimension zero in these algebras.
Abstract
We study the Frobenius-Perron dimension of representation-directed algebras and quotient algebras of canonical algebras of type ADE, prove that the Frobenius-Perron dimension of a representation-directed algebra is always zero and the Frobenius-Perron dimension of a quotient algebra of canonical algebras of type ADE is 0 or 1. Moreover, we give a sufficient and necessary condition for a quotient algebra of a canonical algebra of type ADE under which its Frobenius-Perron dimension is 0.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Rings, Modules, and Algebras