Twisted Conjugacy Classes in Lattices in Semisimple Lie Groups

Abstract

Given a group automorphism $\varphi :\Gamma \to \Gamma$, one has an action of $\Gamma$ on itself by $\varphi$-twisted conjugacy, namely, $g.x=gx\varphi (g^{-1})$. The orbits of this action are called $\varphi$-conjugacy classes. One says that $\Gamma$ has the $R_{\infty }$-property if there are infinitely many $\varphi$-conjugacy classes for every automorphism $\varphi$ of $\Gamma$. In this paper we show that any irreducible lattice in a connected semi simple Lie group having finite centre and rank at least 2 has the $R_{\infty }$-property.

6 pages

References in corpus (1)

• Twisted Conjugacy Classes in Abelian Extensions of Certain Linear Groups

Cited by in corpus (2)

• Twisted Burnside-Frobenius theory for endomorphisms of polycyclic groups
• Twisted conjugacy in classical groups over certain domains of Characteristic $p>0$