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15
105
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Definition of Universal enveloping algebra of a lie algebra

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#abstract-algebra #lie-algebras #equivalence-relations #quotient-spaces
32
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Is the exponential map a global diffeomorphism when g is nilpotent?

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#differential-geometry #lie-groups #lie-algebras
81
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Find an element $x\in\mathfrak{sl}(2,\mathbb{C})$ sucht that the exponential is not a local diffeomorphism at $x$.

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#lie-groups #lie-algebras
60
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Complexification of $G-$representation where $\mathrm{End}_G(V)\cong\mathbb{C}.$

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#representation-theory #lie-groups #lie-algebras
77
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$G$-equivariant map between Lie group representations

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#representation-theory #lie-groups #lie-algebras #semisimple-lie-algebras
110
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Number of type $A_{n-1}$ sub-systems of root system $A_n$

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#abstract-algebra #combinatorics #lie-algebras #root-systems
40
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Isomorphic representation for lie algebra $[x,y]=x$

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#representation-theory #lie-algebras
19
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Semisimple elements in compact Lie groups

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#lie-algebras
29
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When is the simply connected Lie group of a Lie algebra flat?

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#lie-groups #lie-algebras #lie-algebra-cohomology
31
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Equivalence definition to semidirect product in the operated context

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#group-theory #lie-algebras #semigroups #semidirect-product
69
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Vectors belonging to each component of decomposition of semi-simple Lie group representation

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#representation-theory #lie-groups #lie-algebras #semisimple-lie-algebras
57
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Isomorphic connected Lie subgroup

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#lie-groups #lie-algebras
71
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Simple modules of $\mathcal{g}\otimes\mathbb{C}[x]$ for a lie algebra $\mathcal{g}$

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#polynomials #modules #representation-theory #lie-algebras #semisimple-lie-algebras
165
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Lie algebras are to Lie groups what Lie modules are to …?

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#lie-groups #lie-algebras
49
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Lorentz algebra

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#lie-groups #lie-algebras #rotations

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