Operations on the Set of Scalar and Matrix-Valued Quiddity Sequences

Our purpose in this paper is, in the first place, to endow the space of quiddity sequences corresponding to the usual frieze patterns with a SET operad structure, and second to introduce and study \({\mathfrak {M}}\) $\mathfrak{M}$ -quiddity sequences where \({\mathfrak {M}}\) $\mathfrak{M}$ is a monodromy block matrix of order two. Also, we examine related topics such as the possibility of defining matrix-valued friezes patterns and noncommutative signed Chebyshev polynomials.