2019/06/22 by Toshinori Miyatani, Miyatani, Toshinori
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1906.09398
openalex publication_date 2019/06/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.