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Ciro Santilli (@cirosantilli, 34)

Lie algebra exponential covering problem

Lie Groups, Physics, and Geometry by Robert Gilmore (2008) 7.2 "The covering problem" gives some amazing intuition on the subject as usual.

Table of contents
- A single exponential map is not enough to recover a simple Lie group from its algebra Lie algebra exponential covering problem
- The product of a exponential of the compact algebra with that of the non-compact algebra recovers a simple Lie from its algebra Lie algebra exponential covering problem

A single exponential map is not enough to recover a simple Lie group from its algebra

Example at: Lie Groups, Physics, and Geometry by Robert Gilmore (2008) Chapter 7 "EXPonentiation".

The product of a exponential of the compact algebra with that of the non-compact algebra recovers a simple Lie from its algebra

Example at: Lie Groups, Physics, and Geometry by Robert Gilmore (2008) Chapter 7 "EXPonentiation".

Furthermore, the non-compact part is always isomorphic to

R^{n}

, only the non-compact part can have more interesting structure.

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Existence of the matrix logarithm

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