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