TY - UNPB

T1 - Noncommutative frieze patterns with coefficients

AU - Cuntz, Michael

AU - Holm, Thorsten

AU - Jorgensen, Peter

PY - 2024/3/15

Y1 - 2024/3/15

N2 - 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.

AB - 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.

U2 - 10.48550/arXiv.2403.09156

DO - 10.48550/arXiv.2403.09156

M3 - Preprint

BT - Noncommutative frieze patterns with coefficients

ER -