标题： $k$-在特征为2的域上的$\text{SL}(n,k)$的对合 显示英文标题

标题： $k$-involutions of $\text{SL}(n,k)$ over Fields of Characteristic 2

摘要： 对称$k$-流形将黎曼对称空间推广到任意域上定义的约化群。 对于大多数完美域，已知对称$k$-流形与$k$-对合的同构类之间存在一一对应关系。 因此，为了描述$k$-流形，拥有每个同构类的代表是很有用的。 在这里，我们给出$\text{SL}(n,k)$在$k$为特征为 2 的任何域的情况下，$k$-对合每个同构类的矩阵表示；我们还描述了每种类型的对合的固定点群。 显示英文摘要

摘要： Symmetric $k$-varieties generalize Riemannian sym\-me\-tric spaces to reductive groups defined over arbitrary fields. For most perfect fields, it is known that symmetric $k$-varieties are in one-to-one correspondence with isomorphy classes of $k$-involutions. Therefore, it is useful to have representatives of each isomorphy class in order to describe the $k$-varieties. Here we give matrix representatives for each isomorphy class of $k$-involutions of $\text{SL}(n,k)$ in the case that $k$ is any field of characteristic 2; we also describe fixed point groups of each type of involution.