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Quadratic Order of BCH Expansion

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#lie-groups #lie-algebras #matrix-calculus
25
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Why the enveloping algebra of a Lie algebra is a bialgebra?

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#abstract-algebra #lie-algebras #hopf-algebras
68
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Generators of $SU(n)$

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#lie-algebras #unitary-matrices
155
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What is precisely an anti-linear anti-involution?

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#linear-algebra #lie-algebras #universal-algebra #algebras #involutions
212
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"Square root" of a commutator

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#linear-algebra #matrices #lie-algebras
229
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Eigenvalues of Ad$X$ are $\lambda_j-\lambda_k$ where $\lambda_i$'s are those of $X$

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#linear-algebra #matrices #eigenvalues-eigenvectors #lie-algebras #tensor-products
43
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Decomposition of polynomial ring $\mathbb{C}[\mathfrak{gl}_n]$ as a $\mathfrak{gl}_n$-module

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#representation-theory #lie-algebras
163
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Understanding the Lie Algebra of left-invariant vector fields

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#differential-geometry #lie-groups #lie-algebras #smooth-manifolds
92
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$Lie(Ker \pi) = Ker d \pi $

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#differential-geometry #exponential-function #lie-groups #lie-algebras #group-homomorphism
71
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Jordan and Dynkin quivers

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#abstract-algebra #lie-algebras #quiver #dynkin-diagrams #kac-moody-algebras
82
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Definition of a non-split root subgroup

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#algebraic-geometry #representation-theory #lie-algebras #local-field #reductive-groups
65
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Transposition in reductive complex connected groups

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#lie-groups #lie-algebras
50
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How does $\partial_\mu$ act on $A_\nu$ in the local structure equation for a curvature 2-form written in coordinates?

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#differential-geometry #lie-algebras #curvature #connections #principal-bundles
25
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Understanding the Correspondence of Sections to Right and Left Invariant Vector Fields in Ping Xu's 'Momentum Maps and Morita Equivalence

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#differential-geometry #lie-groups #lie-algebras #vector-fields #symplectic-geometry
38
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How to prove this Lie algebra is nilpotent?

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#lie-algebras #nilpotence

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