Bruhat decomposition for long root tori in Chevalley groups

1991 ◽  
Vol 57 (6) ◽  
pp. 3453-3458 ◽  
Author(s):  
N. A. Vavilov ◽  
A. A. Semenov
Keyword(s):  
Bruhat Decomposition ◽  
Chevalley Groups

scholarly journals A family of simple groups associated with the Satake diagrams

1986 ◽  
Vol 41 (1) ◽  
pp. 13-43 ◽  
Author(s):  
Cheng Chonhu
Keyword(s):  
Lie Algebras ◽  
Number Field ◽  
Complex Number ◽  
Algebraic Groups ◽  
Simple Groups ◽  
Orthogonal Groups ◽  
Bruhat Decomposition ◽  
Chevalley Groups ◽  
Complex Number Field ◽  
Real Number Field

AbstractUsing the theory of the Satake diagrams associated with the non-compact simple Lie algebras over the real number field R, we shall construct a family of simple groups over a field K which are called the simple groups associated with the Satake diagrams. The list of these simple groups includes all Chevalley groups and twisted groups, and all simple algebraic groups of adjoint type defined over R if K is the complex number field C (except two types given by Table II′). Furthermore, the simple groups associated with the Satake diagrams of type AIII, BI, DI are identified with the simple groups obtained from the unitary or orthogonal groups of non-zero indices. The quasi-Bruhat decomposition of the “non-split” simple groups associated with the Satake diagrams which are not Chevalley groups or twisted groups will be given in this paper.

Bruhat decomposition for carpet subgroups of Chevalley groups over fields

2021 ◽  
Vol 60 (5) ◽  
pp. 497-509
Author(s):  
Ya. N. Nuzhin ◽  
A. V. Stepanov
Keyword(s):  
Bruhat Decomposition ◽  
Chevalley Groups

scholarly journals 1-Cohomology of Chevalley groups

1989 ◽  
Vol 127 (2) ◽  
pp. 353-372 ◽  
Author(s):  
Helmut Völklein
Keyword(s):  
Chevalley Groups

Elements of Order Coxeter Number +1 in Chevalley Groups

1982 ◽  
Vol 34 (4) ◽  
pp. 945-951 ◽  
Author(s):  
Bomshik Chang
Keyword(s):  
Weyl Group ◽  
Chevalley Group ◽  
Trivial Solution ◽  
Affirmative Answer ◽  
Chevalley Groups ◽  
General Solutions ◽  
Coxeter Number ◽  
Image Position

Following the notation and the definitions in [1], let L(K) be the Chevalley group of type L over a field K, W the Weyl group of L and h the Coxeter number, i.e., the order of Coxeter elements of W. In a letter to the author, John McKay asked the following question: If h + 1 is a prime, is there an element of order h + 1 in L(C)? In this note we give an affirmative answer to this question by constructing an element of order h + 1 (prime or otherwise) in the subgroup Lz = 〈xτ(1)|r ∈ Φ〉 of L(K), for any K.Our problem has an immediate solution when L = An. In this case h = n + 1 and the (n + l) × (n + l) matrixhas order 2(h + 1) in SLn+1(K). This seemingly trivial solution turns out to be a prototype of general solutions in the following sense.

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