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Holonomy theorem for finite semigroups

Published:2022-01-31 Issue:03 Volume:32 Page:443-460
ISSN:0218-1967
Container-title:International Journal of Algebra and Computation
language:en
Short-container-title:Int. J. Algebra Comput.

Author:

Rhodes John¹,Schilling Anne²,Silva Pedro V.³

Affiliation:

1. Department of Mathematics, University of California, Berkeley, CA 94720, USA

2. Department of Mathematics, UC Davis, One Shields Ave., Davis, CA 95616-8633, USA

3. Centro de Matemática, Faculdade de Ciências, Universidade do Porto, R. Campo Alegre 687, 4169-007 Porto, Portugal

Abstract

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.

Funder

NSF

Publisher

World Scientific Pub Co Pte Ltd

Subject

General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218196722500217

Reference14 articles.

1. Markov chains, ${\mathscr R}$-trivial monoids and representation theory

2. Directed Nonabelian Sandpile Models on Trees

3. Encyclopedia of Mathematics and its Applications;Berstel J.,2010

4. Abstract length functions in groups

5. Exact sampling with coupled Markov chains and applications to statistical mechanics

Cited by 1 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Upper Bounds on Mixing Time of Finite Markov Chains;SIAM Journal on Discrete Mathematics;2022-12

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