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Existence of a Parallel Orthonormal Frame Implies Manifold is Flat?

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#differential-geometry #lie-groups #riemannian-geometry #smooth-manifolds
45
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Representation $A$ of a group $G$ on a vector space ${\mathbb{V}}$ is equiv. to a representation on the maps $\varphi:\, G\longrightarrow{\mathbb{V}}$

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#group-theory #finite-groups #representation-theory #lie-groups
36
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A property of orthogonal matrix

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#linear-algebra #lie-groups #orthogonal-matrices
265
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Taylor series using Lie derivatives

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#taylor-expansion #lie-groups #lie-derivative
26
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Left actions of quotient maps

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#lie-groups #quotient-spaces #quotient-group
51
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Understanding Homogeneous spaces

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#lie-groups #homogeneous-spaces
127
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Jacobian Matrix and Exponential Map?

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#lie-groups #jacobian #matrix-exponential #diffeomorphism
277
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Symmetric square of the fundamental representation of $SU(2)$ is irreducible

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#group-theory #representation-theory #lie-groups #lie-algebras #symmetric-algebra
122
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The 5 dimensional irreducible representation of $A_5$

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#group-theory #representation-theory #lie-groups #lie-algebras #symmetric-groups
392
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Inner Product on Lie Algebra So the Exponential Map Becomes the Matrix Exponential?

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#differential-topology #lie-groups #riemannian-geometry #lie-algebras
67
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Group of $2\times2$ matrices that are isomorphic to $SU(2)$

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#group-theory #lie-groups #lie-algebras #linear-groups #unitary-matrices
41
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Transformation of Lie Algebra By Modifying Generating Vector Fields

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#lie-groups #lie-algebras #matrix-calculus #vector-fields #jacobian
70
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An action of Lie group and cohomology

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#lie-groups #smooth-manifolds #group-actions #de-rham-cohomology
44
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Normalization of Generators in SU(N)

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#group-theory #representation-theory #lie-groups #lie-algebras #diagonalization
370
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Compute SO(3) action orbits and stabilizers with representation theory

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#representation-theory #lie-groups #group-actions

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