Number of ends of conjugacy diagrams

Abstract

For each $n\geq 2$, we construct a finitely generated group $W_n$ with a conjugacy class such that the conjugacy diagram of this class has exactly $n$ ends. For this class, we compute the quotient spaces of the space of derivations of the group algebra $\mathbb{C}[W_n]$ modulo quasi-inner and inner derivations, as well as the corresponding component of the first Hochschild cohomology.