Noncommutative frieze patterns with coefficients

verfasst von

Michael Cuntz, Thorsten Holm, Peter Jorgensen

Abstract

Based on Berenstein and Retakh's notion of noncommutative polygons we introduce and study noncommutative frieze patterns. We generalize several notions and fundamental properties from the classic (commutative) frieze patterns to noncommutative frieze patterns, e.g. propagation formulae and μ-matrices, quiddity cycles and reduction formulae, and we show that local noncommutative exchange relations and local triangle relations imply all noncommutative exchange relations and triangle relations. Throughout, we allow coefficients, so we obtain generalizations of results from our earlier paper on frieze patterns with coefficients from the commutative to the noncommutative setting.

Organisationseinheit(en)

Institut für Algebra, Zahlentheorie und Diskrete Mathematik

Externe Organisation(en)

Aarhus University

Typ

Preprint

Anzahl der Seiten

18

Publikationsdatum

15.03.2024

Publikationsstatus

Elektronisch veröffentlicht (E-Pub)

Elektronische Version(en)

https://doi.org/10.48550/arXiv.2403.09156 (Zugang: Offen)