English

On PM-monoids and braid PM-monoids

Combinatorics 2019-06-25 v1 Group Theory

Abstract

In this paper, we shall introduce two monoids. One is called a PM-monoid which contains the symmetric group, the other is called a braid PM-monoid which contains the braid group. We shall develop the theory of PM-monoids and that of braid PM-monoids. The PM-monoids is obtained in the context of the compactification of projective linear group defined by Mutsumi Saito. The structure of PM-monoids is described in terms of matched pairs. We can define braid PM-monoid using a presentation for the PM-monoid. As main results, we show that braid PM-monoids are described by geometric braids and we find a solution to the word problem for the braid PM-monoids.

Keywords

Cite

@article{arxiv.1906.09398,
  title  = {On PM-monoids and braid PM-monoids},
  author = {Toshinori Miyatani},
  journal= {arXiv preprint arXiv:1906.09398},
  year   = {2019}
}

Comments

22 pages, 13 figures

R2 v1 2026-06-23T10:00:33.038Z