A Survey of Lie Groups and Lie Algebras with Applications and Computational Methods.

1973 ◽  
Vol 136 (3) ◽  
pp. 461
Author(s):  
P. Holgate ◽  
Johan G. F. Belinfante ◽  
Bernard Kolman
Keyword(s):  
Lie Groups ◽  
Lie Algebras ◽  
Computational Methods

A Survey of Lie Groups and Lie Algebras with Applications and Computational Methods.

1991 ◽  
Vol 56 (194) ◽  
pp. 886
Author(s):  
Huib-Jan Imbens ◽  
Johan G. F. Belinfante ◽  
Bernard Kolman
Keyword(s):  
Lie Groups ◽  
Lie Algebras ◽  
Computational Methods

scholarly journals Representations of complex semisimple Lie groups and Lie algebras

1966 ◽  
Vol 72 (3) ◽  
pp. 522-526 ◽  
Author(s):  
K. R. Parthasarathy ◽  
R. Ranga Rao ◽  
V. S. Varadarajan
Keyword(s):  
Lie Groups ◽  
Lie Algebras ◽  
Semisimple Lie Groups ◽  
Complex Semisimple

Harmonicity of vector fields on a class of Lorentzian solvable Lie groups

2018 ◽  
Vol 18 (3) ◽  
pp. 337-344 ◽  
Author(s):  
Ju Tan ◽  
Shaoqiang Deng
Keyword(s):  
Vector Field ◽  
Lie Groups ◽  
Lie Algebras ◽  
Critical Points ◽  
Vector Fields ◽  
Energy Functional ◽  
Smooth Vector ◽  
Solvable Lie Groups ◽  
Invariant Vector ◽  
Invariant Vector Fields

AbstractIn this paper, we consider a special class of solvable Lie groups such that for any x, y in their Lie algebras, [x, y] is a linear combination of x and y. We investigate the harmonicity properties of invariant vector fields of this kind of Lorentzian Lie groups. It is shown that any invariant unit time-like vector field is spatially harmonic. Moreover, we determine all vector fields which are critical points of the energy functional restricted to the space of smooth vector fields.

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