scholarly journals Direct Limits of Infinite-Dimensional Lie Groups

2010 ◽  
pp. 243-280 ◽  
Author(s):  
Helge Glöckner
Keyword(s):  
Lie Groups ◽  
Infinite Dimensional ◽  
Direct Limits ◽  
Infinite Dimensional Lie Groups

The theory of infinite-dimensional lie groups and its applications

1985 ◽  
Vol 3 (1) ◽  
pp. 71-106 ◽  
Author(s):  
Osamu Kobayashi ◽  
Akira Yoshioka ◽  
Yoshiaki Maeda ◽  
Hideki Omori
Keyword(s):  
Lie Groups ◽  
Infinite Dimensional ◽  
Infinite Dimensional Lie Groups

scholarly journals Infinite-Dimensional Lie Groups and Algebras in Mathematical Physics

2010 ◽  
Vol 2010 ◽  
pp. 1-35 ◽  
Author(s):  
Rudolf Schmid
Keyword(s):  
Lie Groups ◽  
Mathematical Physics ◽  
Quantum Field ◽  
Loop Groups ◽  
Diffeomorphism Groups ◽  
Gauge Groups ◽  
Infinite Dimensional ◽  
Lie Groups And Algebras ◽  
Volume Preserving ◽  
Infinite Dimensional Lie Groups

We give a review of infinite-dimensional Lie groups and algebras and show some applications and examples in mathematical physics. This includes diffeomorphism groups and their natural subgroups like volume-preserving and symplectic transformations, as well as gauge groups and loop groups. Applications include fluid dynamics, Maxwell's equations, and plasma physics. We discuss applications in quantum field theory and relativity (gravity) including BRST and supersymmetries.

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