List questions from lie-groups

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an equation in a component of identity in a lie group

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Why is the name general "linear" group?

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confused in the term "closed" in closed subgroup

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List Question

Fundamental group of $SO(3)$

Non surjectivity of the exponential map to GL(2,R)

an equation in a component of identity in a lie group

Prove that $O(n)$ is a maximal compact subgroup of $GL(n,\mathbb R)$

What are some examples of nilpotent Lie algeras?

Weyl character formula for locally compact Lie groups.

Fundamental vector fields

From $\mathfrak{so}(16)$ to $\mathfrak{su}(11)$?

Is there a non-matrix Lie group?

Definition of differential of Adjoint representation of Lie Group

What is meant by "tangent space at identity of a Lie group is canonically isomorphic to its Lie algebra"?

Matrix Lie group counter-example: $e^X$ in the Lie group, but $X$ is not in the Lie algebra

Why is the name general "linear" group?

confused in the term "closed" in closed subgroup

Pushforward of inverse map at the identity?

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