Certain invariants of generic matrix algebras

Abstract

Let $K$ be a field of characteristic zero, $W$ be the associative unital algebra generated by two generic traceless matrices $X,$ $Y.$ We also handle the Lie subalgebra $L$ of the algebra $W$ consisting of its Lie elements. Consider the subgroup $G=\langle e_{21}-e_{12}\rangle$ of the special linear group $SL_2(K)$ of order 4. In this study, we give free generators of the algebras $W^G$ and $L^G$ of invariants of the group $G$ as a $C(W)^G$-module.