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Why or how to prove that the infinitesimal symmetries of a differential equation form a Lie algebra?

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#differential-geometry #partial-differential-equations #lie-groups #lie-algebras #symmetry
59
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What does "extend the identity function" mean?

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#lie-groups #lie-algebras
86
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When is the quotient of $\operatorname{GL}_n(\mathbb{R})$ by a discrete subgroup compact?

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#reference-request #lie-groups #homogeneous-spaces #general-linear-group #lattices-in-lie-groups
41
Views

How we define the Lie symmetry of a stochastic differential equation?

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#lie-groups #lie-algebras #stochastic-differential-equations #symmetry #invariant-theory
66
Views

Proving a Maurer-Cartan type equation without differential forms

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#differential-geometry #lie-groups
83
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Why is the diffeomorphism group a manifold?

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#differential-geometry #lie-groups #diffeomorphism
78
Views

Double cover vs universal cover for ${\rm SO}^+(p,q)$

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#group-theory #representation-theory #lie-groups #covering-spaces
79
Views

Why is the complex Lie group $(\mathbb C^*)^n$ called "Complex Torus"

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#lie-groups #complex-geometry #complex-manifolds
23
Views

What is the definition of an affine $G$-module?

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#modules #representation-theory #lie-groups #group-cohomology
61
Views

Proof that $O_3$ and $GL_3$ are homotopy equivalent

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#algebraic-topology #lie-groups
42
Views

How to define periodicity of orbits for general group actions?

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#lie-groups #dynamical-systems #homogeneous-spaces
48
Views

A confusion about Lie group of two dim non abelian real Lie algebra

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#lie-groups #lie-algebras
53
Views

Identity regarding the differential of a smooth action of a Lie group

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#differential-geometry #solution-verification #lie-groups #differential
113
Views

Is $SL(2,\Bbb R)$ generated by $SO(2)$ and a single upper triangular element?

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#matrices #group-theory #lie-groups #matrix-decomposition
416
Views

Smallest group acting transitively on projective space

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#group-theory #algebraic-geometry #finite-groups #representation-theory #lie-groups

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