A1 Subgroups of Exceptional Algebraic Groups - Couverture souple

Lawther, R.; Testerman, D.M.

Couverture souple

ISBN 10 : 0821819666 ISBN 13 : 9780821819661

Editeur : American Mathematical Society, 1999

Synopsis

Abstract - Let $G$ be a simple algebraic group of exceptional type over an algebraically closed field of characteristic $p$. Under some mild restrictions on $p$, we classify all conjugacy classes of closed connected subgroups $X$ of type $A_1$; for each such class of subgroups, we also determine the connected centralizer and the composition factors in the action on the Lie algebra ${\mathcal L}(G)$ of $G$. Moreover, we show that ${\mathcal L}(C_G(X))=C_{{\mathcal L}(G)}(X)$ for each subgroup $X$.These results build upon recent work of Liebeck and Seitz, who have provided similar detailed information for closed connected subgroups of rank at least $2$. In addition, for any such subgroup $X$ we identify the unipotent class ${\mathcal C}$ meeting it. Liebeck and Seitz proved that the labelled diagram of $X$, obtained by considering the weights in the action of a maximal torus of $X$ on ${\mathcal L}(G)$, determines the ($\mathrm{Aut}\,G$)-conjugacy class of $X$. We show that in almost all cases the labelled diagram of the class ${\mathcal C}$ may easily be obtained from that of $X$; furthermore, if ${\mathcal C}$ is a conjugacy class of elements of order $p$, we establish the existence of a subgroup $X$ meeting $${\mathcal C}$ and having the same labelled diagram as ${\mathcal C}$.

Détails de l'édition

• Éditeur: American Mathematical Society
• Date d'édition: 1999
• Langue: anglais
• ISBN 10: 0821819666
• ISBN 13: 9780821819661
• Reliure: Broché
• Nombre de pages: 131
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible