The Reductive Subgroups of F_4
Seiten
2013
American Mathematical Society (Verlag)
978-0-8218-8332-7 (ISBN)
American Mathematical Society (Verlag)
978-0-8218-8332-7 (ISBN)
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Let G=G(K) be a simple algebraic group defined over an algebraically closed field K of characteristic p≥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=F4(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 A1 this gives a complete classification of the simple subgroups of G.
The author also uses this classification to find all subgroups of G=F4 which are generated by short root elements of G, by utilising and extending the results of Liebeck and Seitz.
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 A1 this gives a complete classification of the simple subgroups of G.
The author also uses this classification to find all subgroups of G=F4 which are generated by short root elements of G, by utilising and extending the results of Liebeck and Seitz.
David I. Stewart, New College, Oxford, United Kingdom.
Table of Contents
Introduction
Overview
General Theory
Reductive subgroups of $F_4$
Appendices
Bibliography
| Erscheint lt. Verlag | 30.7.2013 |
|---|---|
| Reihe/Serie | Memoirs of the American Mathematical Society |
| Verlagsort | Providence |
| Sprache | englisch |
| Gewicht | 200 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| ISBN-10 | 0-8218-8332-1 / 0821883321 |
| ISBN-13 | 978-0-8218-8332-7 / 9780821883327 |
| Zustand | Neuware |
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