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Can some one kindly go over some of the applications and use of Lie groups in finance? The math is very rigorous and I don't fully understand it or the potential it could have.

Let me share some examples with you, I'm sure there are many more. There even is a financial math graduate program in Europe where there is required course work that teaches Lie groups.

http://www.sciencedirect.com/science/article/pii/S0096300308009156

http://math.sut.ac.th/school/faculty/sergey/filespublic/2006/SrihirunMeleshkoSchultz2006_I.pdf

http://www.phy.cuhk.edu.hk/~cflo/Finance/papers/publications/lie_QF.pdf

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    $\begingroup$ Could you please explain what lie groups are and why you think it's applicable to finance (suggest areas of application})? This would make a much better question and it would be much more useful for other users of the site. $\endgroup$
    – SRKX
    Commented Apr 20, 2012 at 6:21
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    $\begingroup$ Please provide a link to a finance article that makes explicit use of lie group theory $\endgroup$
    – Alexey Kalmykov
    Commented Apr 20, 2012 at 10:22
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    $\begingroup$ Where did you see this? I've never heard of lie groups applied to finance. $\endgroup$
    – chrisaycock
    Commented Apr 20, 2012 at 12:49
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    $\begingroup$ Well, we do use $\mathbb{R}^n$ all the time. $\endgroup$
    – Brian B
    Commented Apr 20, 2012 at 15:49
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    $\begingroup$ I've updated the question with some papers $\endgroup$
    – pyCthon
    Commented Apr 21, 2012 at 18:38

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I didn't read the papers you linked but I can understand that lie groups may be used much as there are used in quantum field theories to build up gauge theories for interaction of particles. The purpose is to have a model that is invariant according to a given transformation group. This introduce interaction terms in the equations.

I can imagine that the same technique can be used in financial stochastic processes to force the introduction of new terms in the equations.

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