Noncommutative frieze patterns with coefficients

authored by

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.

Organisation(s)

Institute of Algebra, Number Theory and Discrete Mathematics

External Organisation(s)

Aarhus University

Type

Preprint

No. of pages

18

Publication date

15.03.2024

Publication status

E-pub ahead of print

Electronic version(s)

https://doi.org/10.48550/arXiv.2403.09156 (Access: Open)