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Quotient of semidirect product by one of its factors

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#abstract-algebra #group-theory #lie-groups
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Infinite root systems

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#abstract-algebra #group-theory #lie-groups #lie-algebras #infinitary-combinatorics
3.6k
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Why is a simply connected Lie group determined by its Lie algebra?

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#lie-groups #lie-algebras
112
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Exponential map from loop algebras to loop groups

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#lie-groups #lie-algebras #infinite-groups
946
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Relation between definitions of Lie bracket via adjoint representation and via left-invariant vector fields

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#abstract-algebra #differential-geometry #manifolds #lie-groups #lie-algebras
745
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Embedding of symmetric groups into orthogonal groups

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#group-theory #permutations #lie-groups #symmetric-groups #group-actions
186
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Orbit under Lie group and projective variety

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#algebraic-geometry #lie-groups #homogeneous-spaces
576
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Every positive system of roots contains a unique simple system.

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#lie-groups #lie-algebras #reflection #root-systems #coxeter-groups
1.5k
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Reduction of Principal bundle's

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#geometry #algebraic-geometry #differential-geometry #differential-topology #lie-groups
1.1k
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$\mathfrak{sp}(4,\mathbb{R})$ isomorphic to $\mathfrak{so}(5,\mathbb{R})$.

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#lie-groups #lie-algebras
155
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Weyl character formula and Harish-Chandra isomorphism

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#lie-groups #lie-algebras
99
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An example of a representation which is simultaneously of real and quaternionic type

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#representation-theory #lie-groups
800
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How to construct the matrix Lie group from the corresponding Lie algebra, using the exponential map?

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#lie-groups #lie-algebras
174
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Root system for Lie algebras, Does $t_{\alpha+\beta}=t_\alpha+t_\beta$?

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#lie-groups #lie-algebras #root-systems
593
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Find a Cartan subalgebra of ${\frak so}_{2n}(\mathbb C)$

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#lie-groups #lie-algebras

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