Isomorphism classes of \(k\)-involutions of algebraic groups of type \(\mathrm F_4\). (Q2791846)

The author deals with several aspects of algebraic groups of type \(\mathrm F_4\). Many concepts are involved in the development of the contents of this paper, such as the split Albert algebra, the Jordan algebra, the quaternion algebra, and the octonion algebra. The author uses many results of several of the papers that he quotes in the present article.NEWLINENEWLINE The main result obtained by the author is a full classification of \(k\)-involutions of algebraic groups of type \(\mathrm F_4\) for \(k=K,\mathbb R,\mathbb Q_p\), and \(\mathbb F_q\) for \(p\geq 2\) and \(q>2\), where \(K\) is the algebraic closure of \(k\).