scholarly journals Semisimple groups that are quasi-split over a tamely ramified extension

2018 ◽  
Vol 140 ◽  
pp. 173-183
Author(s):  
Philippe Gille
Keyword(s):  
Semisimple Groups

Extension of Elliott's projection technique to compact semisimple groups

Physica ◽  
1974 ◽  
Vol 73 (3) ◽  
pp. 585-592
Author(s):  
M. Bouten ◽  
D. Haentjens ◽  
P. Van Leuven
Keyword(s):  
Projection Technique ◽  
Semisimple Groups

Automorphisms, isomorphisms, and Tits classification

2015 ◽  
Author(s):  
Brian Conrad ◽  
Gopal Prasad
Keyword(s):  
Affine Group ◽  
Classification Theorem ◽  
Isomorphism Theorem ◽  
Reductive Groups ◽  
Semisimple Groups ◽  
Dynkin Diagrams ◽  
Weil Restriction ◽  
Characteristic 2 ◽  
Smooth Affine

This chapter considers automorphisms, isomorphisms, and Tits classification. It begins by establishing a version of the Isomorphism Theorem for pseudo-split pseudo-reductive groups, along with a pseudo-reductive variant of the Isogeny Theorem for split connected semisimple groups. The key to both proofs is a technique to construct pseudo-reductive subgroups of an ambient smooth affine group. Some instructive examples over imperfect fields k of characteristic 2 are given. The chapter goes on to discuss the behavior of the k-group ZG,C with respect to Weil restriction in the pseudoreductive case. It also describes automorphism schemes for pseudo-reductive groups, focusing only on the pseudo-semisimple case because commutative pseudo-reductive groups that are not tori generally have a non-representable automorphism functor. Finally, it examines Tits-style classification, using Dynkin diagrams to express the classification theorem.

scholarly journals On non-Abelian T-duality for non-semisimple groups

2018 ◽  
Vol 78 (12) ◽  
Author(s):  
Moonju Hong ◽  
Yoonsoo Kim ◽  
Eoin Ó Colgáin
Keyword(s):  
Semisimple Groups
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