On commutative set-theoretic solutions of the Pentagon Equation

2024/04/21 by Marco Castelli, Castelli, Marco · 1 citation
Computer Science · Engineering · Mathematics · #81R50 20M99 #Elasticity and Wave Propagation #FOS: Mathematics #Mathematical Control Systems and Analysis #Mathematics and Applications #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.2404.13758

openalex publication_date 2024/04/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We extend the so-called retract relation given in [6] for involutive set-theoretic solutions of the Pentagon Equation and we introduce the notion of associated permutation group to study the family of the commutative non-degenerate ones. Moreover, we develop a machinery to construct all these solutions and we use it to give a quite explicit classification of the irretractable ones. Finally, non-degenerate solutions on left-zero semigroup are studied in detail, with an emphasis on the ones with cyclic associated permutation group and on the ones having small size.

Cited by

• Associative Pentagon Algebras

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