- #1
JTC
- 100
- 6
Good Day
I have been having a hellish time connection Lie Algebra, Lie Groups, Differential Geometry, etc.
But I am making a lot of progress.
There is, however, one issue that continues to elude me.
I often read how Lie developed Lie Groups to study symmetries of PDE's
May I ask if someone could exemplify this with a very simple, concrete example?
For example, I understand orthogonal matrices (Lie Groups) and how their basis is skew symmetric matrices as generators (Lie Algebras) and I can connect this with the need to study Differential geometry.
But where can I find (or could someone provide) a simple, example of how rotation matrices preserve symmetries of PDS (and, also, explain what a synmmetry of a PDE is)
I have been having a hellish time connection Lie Algebra, Lie Groups, Differential Geometry, etc.
But I am making a lot of progress.
There is, however, one issue that continues to elude me.
I often read how Lie developed Lie Groups to study symmetries of PDE's
May I ask if someone could exemplify this with a very simple, concrete example?
For example, I understand orthogonal matrices (Lie Groups) and how their basis is skew symmetric matrices as generators (Lie Algebras) and I can connect this with the need to study Differential geometry.
But where can I find (or could someone provide) a simple, example of how rotation matrices preserve symmetries of PDS (and, also, explain what a synmmetry of a PDE is)