Non-crossing partitions of type (e,e,r)

David Bessis; Ruth Corran

Non-crossing partitions of type (e,e,r)

Group Theory 2007-05-23 v2

Authors: David Bessis , Ruth Corran

Abstract

We investigate a new lattice of generalised non-crossing partitions, constructed using the geometry of the complex reflection group $G(e,e,r)$ . For the particular case $e=2$ (resp. $r=2$ ), our lattice coincides with the lattice of simple elements for the type $D_n$ (resp. $I_2(e)$ ) dual braid monoid. Using this lattice, we construct a Garside structure for the braid group $B(e,e,r)$ . As a corollary, one may solve the word and conjugacy problems in this group.

Keywords

noncrossing partitions braid groups lattice theory

Cite

@article{arxiv.math/0403400,
  title  = {Non-crossing partitions of type (e,e,r)},
  author = {David Bessis and Ruth Corran},
  journal= {arXiv preprint arXiv:math/0403400},
  year   = {2007}
}

Comments

38 pages, 15 figures; second version with extended introduction

Non-crossing partitions of type (e,e,r)

Abstract

Keywords

Cite

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