2025/05/19 by Carsten Dietzel, Dietzel, Carsten
Mathematics · #06B99 #06F15 #20F36 #20N99 #Advanced Operator Algebra Research #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2505.13347
openalex publication_date 2025/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work, we address a question posed by Dehornoy et al. in the book "Foundations of Garside Theory" that asks for a theory of groups of IG-type when G is a Garside group. In this article, we introduce a broader notion than the one suggested by Dehornoy et al.: given a left-ordered group G, we define a group of IG-type as a left-ordered group whose partial order is isomorphic to those of G. Furthermore, we develop methods to give a characterization of groups of IΓ-type in terms of skew braces when Γ is an Artin-Tits group of spherical type and classify all groups of IΓ-type where Γ is an irreducible spherical Artin-Tits group, therefore providing an answer to another question of Dehornoy et al. concerning IBn structures where Bn is the braid group on n strands with its canonical Garside structure.