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Projectivity of $U(\mathfrak(g))$ as a $U(\mathfrak(b))$-module

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#ring-theory #representation-theory #lie-algebras #tensor-products
226
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How to derive the formula $\{t_{ij}, t_{kl}\} = \sum_{a,b} (r^{ajbl} t_{ia}t_{kb} - r^{iakb} t_{aj}t_{bl})$?

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#lie-groups #lie-algebras #poisson-geometry #integrable-systems
47
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Simply-connectedness condition in Levi-Malcev decomposition theorem

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#manifolds #lie-groups #lie-algebras
322
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Elliptic elements in Weyl groups and corresponding sub-root systems

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#lie-algebras #root-systems #coxeter-groups
316
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tensor product of two representations of simple lie algebra

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#representation-theory #lie-algebras
873
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Example of a nilpotent matrix which is not a nilpotent element of Lie Algebra

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#lie-groups #lie-algebras
414
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tensor product of finite-dimensional irreducible modules for a semisimple Lie algebra

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#representation-theory #lie-algebras
218
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What is the commutator in $gl(m|n)$?

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#abstract-algebra #lie-algebras #superalgebra #lie-superalgebras
267
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Maurer Cartan form and Levi-Civita Connection

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#differential-geometry #lie-groups #riemannian-geometry #lie-algebras
77
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Cartan subalgebras of matrix algebras over fields and division algebras

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#lie-algebras
533
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Components of the Fitting Decomposition for $L$ are Invariant under $M$'s with $ad(L)^sM=0$

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#linear-algebra #representation-theory #lie-algebras #linear-transformations
83
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Smallest orthogonal group that has E8 as a subgroup?

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#lie-groups #lie-algebras
139
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A decomposition of $SO(p,q)$

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#lie-groups #lie-algebras #moduli-space #k3-surfaces
266
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Narasimhan-Seshadri with Arbitrary Structure Group $G$?

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#differential-geometry #algebraic-geometry #representation-theory #lie-algebras #vector-bundles
41
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Why $\partial_i^{[p]} = \partial_i$?

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#field-theory #lie-algebras #partial-derivative

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