On P M-monoids and braid P M-monoids

摘要

In this paper, we shall introduce two monoids. One is called a P M-monoid which contains the symmetric group, the other is called a braid P M-monoid which contains the braid group. We shall develop the theory of P M-monoids and that of braid P M-monoids. A P M-monoid is obtained in the context of a compactification of projective linear group defined by Mutsumi Saito. The structure of a P M-monoid is described in terms of a matched pair. We can define braid P M-monoid in the context of a presentation for a P M-monoid. As main results, we show that braid P M-monoids are described by geometric braids, and we find a solution to the word problem for the braid PM-monoids. (C) 2020 Elsevier B.V. All rights reserved.