Year: 2004
Type: preprint
Abstract: We prove that Thompson's groups $F$ and $V$ are the geometry groups of associativity, and of associativity together with commutativity, respectively. We deduce new presentations of $F$ and $V$. These presentations lead to considering a certain subgroup of $V$ and an extension of this subgroup. We prove that the latter are the geometry groups of associativity together with the law $x(yz) = y(xz)$, and of associativity together with a twisted version of this law involving self-distributivity, respectively.
Source: arXiv (Cornell University)
Author: Dehornoy, Patrick
Institution: Laboratoire de Mathématiques Nicolas Oresme
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2950342416