User:Nerd1a4i/Lie groups

Lie groups are groups that can also be manifolds.

Example

Imagine the points that make up a circle. If you multiply together any of the points on the circle, you get a point that is still on the circle. This means we have created a group whose operation is multiplication and whose elements are the points on a circle. If you look at a very small part of the circle, it looks like a line. This means that it is a manifold. So, the group of points that make up a circle is in fact a Lie group.

History

Lie groups were named after a Norwegian mathematician, Marius Sophus Lie.

Use

Lie groups are useful in different parts of physics because they can represent symmetries in a system.

References

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