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Holonomy theorem for finite semigroups

https://doi.org/10.1142/S0218196722500217

Rhodes, John ; Schilling, Anne ; Silva, Pedro V. ( May 2022 , International Journal of Algebra and Computation)

In this paper, we provide a simple proof of the Holonomy theorem using a new Lyndon–Chiswell length function on the Karnofsky–Rhodes expansion of a semigroup. Unexpectedly, we have both a left and a right action on the Chiswell tree by elliptic maps.
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