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15
126
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Projecting vector field from $\mathbb{R}^n$ to $T^n$

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#manifolds #lie-groups #smooth-manifolds #vector-fields
104
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Index of the congruence subgroups of $PGL_2(\mathbb{Z}_p)$.

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#abstract-algebra #group-theory #number-theory #lie-groups #p-adic-number-theory
58
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When does a simple Lie group contain a nonsimple subgroup?

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#group-theory #lie-groups #simple-groups
86
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How is a group visually represented?

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#general-topology #group-theory #lie-groups
125
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Lie group intuition

Published on
#lie-groups #smooth-manifolds #intuition
42
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Differential of element in the stabiliser

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#lie-groups #smooth-manifolds
547
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$SP_{2n}(\mathbb {R})$ acts transitively on $\mathbb {R}^{2n}$

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#abstract-algebra #group-theory #lie-groups #symplectic-linear-algebra
405
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How to prove that $GL(V)$ is a Lie-group without a choice of a basis.

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#linear-algebra #group-theory #lie-groups
80
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If $\exp(X) \in G$, and $X$ is Hermitian, do we have $X \in \mathfrak g$?

Published on
#differential-geometry #lie-groups #algebraic-groups
223
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Matrix lie algebra automorphisms

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#matrices #lie-groups #lie-algebras
1.1k
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A discrete normal subgroup is contained in the center

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#abstract-algebra #group-theory #lie-groups
164
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Representation of a Lie algebra over the space of smooth functions.

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#functional-analysis #differential-geometry #lie-groups #lie-algebras #smooth-manifolds
29
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Complex smooth maps over $(0 , \infty) \times G$.

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#differential-geometry #lie-groups #smooth-manifolds #smooth-functions
1.7k
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The Lie bracket of $\mathfrak{gl}_n(\mathbb{R})$ is the matrix commutator

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#differential-geometry #lie-groups #lie-algebras #smooth-manifolds
28
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Relationship between Carnot-Caratheory Distance and Levi-Civita Connection

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#lie-groups #riemannian-geometry #connections #nilpotent-groups

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