The $R_{\infty}$ and $S_{\infty}$ properties for linear algebraic groups

TL;DR

This paper investigates properties related to automorphisms of reductive linear algebraic groups, demonstrating that such groups over certain fields exhibit the $R_ty$ and $S_ty$ properties, which relate to twisted conjugacy classes.

Contribution

It establishes that reductive linear algebraic groups over some fields of zero characteristic have the $R_ty$ and $S_ty$ properties, advancing understanding of their automorphism structures.

Findings

Reductive linear algebraic groups over zero characteristic fields have the $R_ty$ property.

Such groups also possess the $S_ty$ property.

The study of twisted conjugacy classes is extended to these groups.

Abstract

In the paper we study twisted conjugacy classes and isogredience classes for automorphisms of reductive linear algebraic groups. We show that reductive linear algebraic groups over some fields of zero characteristic possess the $R_\infty$ and $S_\infty$ properties.