Matrix factorizations and pentagon maps

Abstract

We propose a specific class of matrices which participate in factorization problems that turn to be equivalent to constant and entwining (non-constant) pentagon, reverse-pentagon or Yang-Baxter maps, expressed in non-commutative variables. In detail, we show that factorizations of order $N=2$ matrices of this specific class are equivalent to the homogeneous normalization map. From order $N=3$ matrices, we obtain an extension of the homogeneous normalization map, as well as novel entwining pentagon, reverse-pentagon and Yang-Baxter maps.

arXiv comment14 pages, 2 figures. v2: Typos corrected

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Cited by in corpus (2)

• On the Structure of Set-Theoretic Polygon Equations
• Set-theoretical solutions to the pentagon equation: a survey