The reductive subgroups of F₄
Science Library (Li and Ma)
|Shelved by Series title NO.1049||Unknown|
- Stewart, David I., 1981-
- Includes bibliographical references and index.
- Table of Contents * Introduction * Overview * General Theory * Reductive subgroups of $F_4$ * Appendices * Bibliography.
- (source: Nielsen Book Data)9780821883327 20160612
- Publisher's Summary
- 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.
(source: Nielsen Book Data)9780821883327 20160612
- Publication date
- Title Variation
- Reductive subgroups of F4
- Memoirs of the American Mathematical Society, 0065-9266 ; number 1049
- "May 2013, volume 223, number 1049 (third of 5 numbers)."
- 9780821883327 (alk. paper)
- 0821883321 (alk. paper)
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