The orbit method. II. Infinite-dimensional Lie groups and Lie algebras

1993 ◽  
pp. 33-63 ◽  
Author(s):  
Aleksandr Kirillov
Keyword(s):  
Lie Groups ◽  
Lie Algebras ◽  
Orbit Method ◽  
Infinite Dimensional ◽  
Infinite Dimensional Lie Groups

scholarly journals Pro-Lie groups which are infinite-dimensional Lie groups

2009 ◽  
Vol 146 (2) ◽  
pp. 351-378 ◽  
Author(s):  
K. H. HOFMANN ◽  
K.-H. NEEB
Keyword(s):  
Lie Groups ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Exponential Function ◽  
Lie Group ◽  
Smooth Manifold ◽  
Projective Limit ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Infinite Dimensional Lie Groups

AbstractA pro-Lie group is a projective limit of a family of finite-dimensional Lie groups. In this paper we show that a pro-Lie group G is a Lie group in the sense that its topology is compatible with a smooth manifold structure for which the group operations are smooth if and only if G is locally contractible. We also characterize the corresponding pro-Lie algebras in various ways. Furthermore, we characterize those pro-Lie groups which are locally exponential, that is, they are Lie groups with a smooth exponential function which maps a zero neighbourhood in the Lie algebra diffeomorphically onto an open identity neighbourhood of the group.

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.

Sign in / Sign up

Export Citation Format

Share Document