Word and Conjugacy Problems in Groups $G_{k+1}^{k}$
Abstract
Recently the third named author defined a 2-parametric family of groups \cite{gnk}. Those groups may be regarded as a certain generalisation of braid groups. Study of the connection between the groups and dynamical systems led to the discovery of the following fundamental principle: `If dynamical systems describing the motion of particles possess a nice codimension one property governed by exactly particles, then these dynamical systems admit a topological invariant valued in '. The groups have connections to different algebraic structures, Coxeter groups and Kirillov-Fomin algebras, to name just a few. Study of the groups led to, in particular, the construction of invariants, valued in free products of cyclic groups. In the present paper we prove that word and conjugacy problems for certain groups are algorithmically solvable, and the algorithms are constructive.
Cite
@article{arxiv.1906.04916,
title = {Word and Conjugacy Problems in Groups $G_{k+1}^{k}$},
author = {Denis Fedoseev and Andrey Karpov and Vassily Manturov},
journal= {arXiv preprint arXiv:1906.04916},
year = {2019}
}
Comments
arXiv admin note: substantial text overlap with arXiv:1905.08049, arXiv:1803.01195. Author note: arXiv:1905.08049 is a Survey, which describes what is done in the field, including the results of this paper; arXiv:1803.01195 is an earlier work by one of the authors, which is used as a background and source of definitions in the present paper