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Lie Groups are Groups that are additionally smooth manifolds such that the multiplication and the inverse maps are smooth.

5 votes

Lie group about the quantum harmonic oscillator

The oscillator group, of course. See Streater, The representations of the oscillator group, Communications in Mathematical Physics 1967, Volume 4, Issue 3, pp 217-236, for a description of its represe …
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6 votes

Reference requested: Random walk on groups

How about these two books for a start? Tullio Ceccherini-Silberstein, Fabio Scarabotti, and Filippo Tolli. Harmonic analysis on finite groups. Representation theory, Gelfand pairs and Markov chains. …
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3 votes
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Reference to definition of matrix log with domain SO(3) which is Borel measurable

Have a look at the paper COMPUTING EXPONENTIALS OF SKEW-SYMMETRIC MATRICES AND LOGARITHMS OF ORTHOGONAL MATRICES by J. Gallier and D. Xu (International Journal of Robotics and Automation, Vol. 17, No. …
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