Representations of field automorphism groups

Cluster automorphism groups and automorphism groups of exchange graphs

For a coefficient free cluster algebra $\mathcal{A}$, we study the cluster automorphism group $Aut(\mathcal{A})$ and the automorphism group $Aut(E_{\mathcal{A}})$ of its exchange graph $E_{\mathcal{A}}$. We show that these two groups are isomorphic with each other, if $\mathcal{A}$ is of finite type excepting types of rank two and type $F_4$, or if $\mathcal{A}$ is of skew-symmetric finite mutation type.

Group Extensions and Automorphism Group Rings

The group ring of the automorphism group of a p-group is studied using the automorphism groups of subgroups and quotient groups of P.

A Kazhdan group with an infinite outer automorphism group

D. Kazhdan has introduced in 1967 the Property (T) for local compact groups. In this article we prove that for $n\geq 3$ and $m \in \mathbb{N}$ the group $SL_n(\textbf{K})\ltimes \mathcal{M}_{n,m}(\textbf{K})$ is a Kazhdan group having the outer automorphism group infinite.

函子形变与模的自同构群的表示

Functor morphing and representations of automorphism groups of modules

本文提出利用函子形变研究局部环上有限模自同构群的不可约表示，证明这些群具有层级结构，可借助对称幺半范畴和不变量理论以更小的构建块对其表示进行分层。

The Brauer characters of the sporadic simple Harada-Norton group and its automorphism group in characteristics 2 and 3

We determine the 2-modular and 3-modular character tables of the sporadic simple Harada-Norton group and its automorphism group.

On the Automorphisms and Representations of Polyadic Groups

Using a unified method, we determine the structure of automorphisms and representations of arbitrary polyadic groups. More precisely, for a polyadic group $(G, f)=der_{θ, b}(G, \cdot)$, we obtain a complete description of automorphisms and representations of $(G,f)$ in terms of automorphisms and representations of the binary group $(G, \cdot)$.