Computing Cartan subalgebras of Lie algebras

1996 ◽  
Vol 7 (5) ◽  
pp. 339-349 ◽  
Author(s):  
Willem De Graaf ◽  
Gábor Ivanyos ◽  
Lajos Rónyai
Keyword(s):  
Lie Algebras ◽  
Cartan Subalgebras

Computing Cartan Subalgebras of Lie Algebras

1996 ◽  
Vol 7 (5) ◽  
pp. 339-349
Author(s):  
Willem De Graaf ◽  
G�bor Ivanyos ◽  
Lajos R�nyai
Keyword(s):  
Lie Algebras ◽  
Cartan Subalgebras

scholarly journals Computing with real Lie algebras: Real forms, Cartan decompositions, and Cartan subalgebras

2013 ◽  
Vol 56 ◽  
pp. 27-45 ◽  
Author(s):  
Heiko Dietrich ◽  
Paolo Faccin ◽  
Willem A. de Graaf
Keyword(s):  
Lie Algebras ◽  
Cartan Subalgebras ◽  
Real Forms

Cartan subalgebras of meta-nilpotent Lie algebras

1970 ◽  
Vol 116 (3) ◽  
pp. 215-217 ◽  
Author(s):  
Charles B. Hallahan ◽  
Julius Overbeck
Keyword(s):  
Lie Algebras ◽  
Nilpotent Lie Algebras ◽  
Cartan Subalgebras

Conjugacy Classes of Maximal Tori in Simple Real Algebraic Groups and Applications

1994 ◽  
Vol 46 (4) ◽  
pp. 699-717 ◽  
Author(s):  
Dragomir Ž. Doković ◽  
Nguyêñ Quôć Thăńg
Keyword(s):  
Lie Algebras ◽  
Lie Group ◽  
Short Proof ◽  
Algebraic Groups ◽  
Conjugacy Classes ◽  
Exponential Map ◽  
Simple Complex ◽  
Maximal Tori ◽  
Cartan Subalgebras

AbstractLet G be an almost simple complex algebraic group defined over R, and let G(R) be the group of real points of G. We enumerate the G(R)-conjugacy classes of maximal R-tori of G. Each of these conjugacy classes is also a single G(R)˚-conjugacy class, where G(R)˚ is the identity component of G(R), viewed as a real Lie group. As a consequence we also obtain a new and short proof of the Kostant-Sugiura's theorem on conjugacy classes of Cartan subalgebras in simple real Lie algebras.A connected real Lie group P is said to be weakly exponential (w.e.) if the image of its exponential map is dense in P. This concept was introduced in [HM] where also the question of identifying all w.e. almost simple real Lie groups was raised. By using a theorem of A. Borel and our classification of maximal R-tori we answer the above question when P is of the form G(R)˚.

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