Yokonuma-Hecke algebra

introduction

def (Yokonuma--Hecke algebra)

The Yokonuma--Hecke algebra \(Y_{d,n}\) is generated by elements \[g_1,\ldots,g_{n-1},t_1,\ldots,t_n,\] subject to the following defining relations : \[ \label{def-1} \begin{array}{rclcl} g_ig_j & = & g_jg_i &\ & \mbox{for \]i,j=1,\ldots,n-1\( such that \)\vert i-j\vert > 1\(,}\\ g_ig_{i+1}g_i & = & g_{i+1}g_ig_{i+1} && \mbox{for \)i=1,\ldots,n-2\(,} \end{array} \)

articles

• Ivan Marin, Artin groups and Yokonuma-Hecke algebras, arXiv:1601.03191 [math.RT], January 13 2016, http://arxiv.org/abs/1601.03191