Publication details

Noncommutative frieze patterns with coefficients

authored by
Michael Cuntz, Thorsten Holm, Peter Jorgensen

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.

Institute of Algebra, Number Theory and Discrete Mathematics
External Organisation(s)
Aarhus University
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E-pub ahead of print
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