Reductive Subgroups of $F_4$ (eBook)

David I Stewart (Autor)

eBook Download: PDF

88 Seiten
American Mathematical Society (Verlag)
978-0-8218-9873-4 (ISBN)

Infos

Let $G=G(K)$ be a simple algebraic group defined over an algebraically closed field $K$ of characteristic $p/geq 0$. A subgroup $X$ of $G$ is said to be $G$-completely reducible if, whenever it is contained in a parabolic subgroup of $G$, it is contained in a Levi subgroup of that parabolic. A subgroup $X$ of $G$ is said to be $G$-irreducible if $X$ is in no proper parabolic subgroup of $G$; and $G$-reducible if it is in some proper parabolic of $G$. In this paper, the author considers the case that $G=F_4(K)$. The author finds all conjugacy classes of closed, connected, semisimple $G$-reducible subgroups $X$ of $G$. Thus he also finds all non-$G$-completely reducible closed, connected, semisimple subgroups of $G$. When $X$ is closed, connected and simple of rank at least two, he finds all conjugacy classes of $G$-irreducible subgroups $X$ of $G$. Together with the work of Amende classifying irreducible subgroups of type $A_1$ this gives a complete classification of the simple subgroups of $G$. The author also uses this classification to find all subgroups of $G=F_4$ which are generated by short root elements of $G$, by utilising and extending the results of Liebeck and Seitz.

Produkt-Details

• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• ISBN-10: 0-8218-9873-6 / 0821898736
• ISBN-13: 978-0-8218-9873-4 / 9780821898734