: Mathematics: Lie group

topology > algebraic topology > manifold > differentiable manifold > Lie group

geometry > topological space > manifold > differentiable manifold > Lie group

geometry > differential geometry > differentiable manifold > Lie group

topology > differential topology > differentiable manifold > Lie group

algebra > group theory > topological group > Lie group

Lie group

In mathematics, a Lie group is a group that is also a differentiable manifold. A manifold is a space that locally resembles Euclidean space, whereas groups define the abstract concept of a binary operation along with the additional properties it must have to be thought of as a "transformation" in the abstract sense, for instance multiplication and the taking of inverses (division), or equivalently, the concept of addition and the taking of inverses (subtraction). Combining these two ideas, one obtains a continuous group where multiplying points and their inverses are continuous. If the multiplication and taking of inverses are smooth (differentiable) as well, one obtains a Lie group.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Lie_group)

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