Extended Special Linear group $ESL_2(\mathbb{F})$ and matrix equations in $SL_2(\mathbb{F})$, $SL_2(\mathbb{Z})$ and $GL_2(\mathbb{F}_p)$

by Ruslan Skuratovskii

Wednesday 19 Jun 2024, 16:00 → 17:00 Europe/Kiev

https://bbb.imath.kiev.ua/rooms/boh-0lk-tl9-vjx/join (ONLINE)

The problems of roots existence for different classes of matrix such as simple and semisimple matrixes from $SL_2({\mathbb{F}})$, $ SL_2({\mathbb{Z}})$  and $ GL_2({\mathbb{F}})$ are solved.

First time, we introduce the concept of extended special linear group $ESL_2(\mathbb{F})$, which is generalization of the matrix group $SL_2(\mathbb{F})$, where $\mathbb{F}$ is arbitrary perfect field.

 

The group of unimodular matrices are generalized  by us, their structures are found.