Products of commutators of unipotent matrices of index $2$ in $\\mathrm{GL}_n(\\mathbb H)$

Authors : Ha Nguyen Thi Thai, Dao Trong Toan

Pages : 121-133

Doi:10.24330/ieja.1476670

View : 58 | Download : 101

Publication Date : 2024-07-12

Article Type : Research Paper

Abstract :The aim of this paper is to show that if $\\mathbb{H}$ is the real quaternion division ring and $n$ is an integer greater than $1,$ then every matrix in the special linear group $\\mathrm{SL}_n(\\mathbb{H})$ can be expressed as a product of at most three commutators of unipotent matrices of index $2$.
Keywords : Matrix decomposition, matrix over a division ring, commutator length