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How can we define a $\mathbb{Z}$-grading on sl2

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#lie-algebras #graded-algebras
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Lie Group and Lie Algebra Homomorphisms

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#lie-groups #lie-algebras
610
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Show invariance under linear transformation

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#group-theory #linear-transformations #lie-groups #lie-algebras #mathematical-physics
682
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Definition of reductive homogeneous space

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#differential-geometry #lie-groups #lie-algebras #homogeneous-spaces
358
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Does usual Jordan decomposition be preserved by finite dimensional representation?

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#representation-theory #lie-algebras
67
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killing Form is null for some elements of Lie algebra of symplectic group

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#linear-algebra #lie-groups #lie-algebras #symplectic-linear-algebra
33
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Root system of Lie algebra: right angle => not simple?

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#group-theory #lie-groups #lie-algebras #root-systems
24
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morphism $df : Lie(\Bbb R, +) \to Lie(S^1)$

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#linear-algebra #lie-groups #lie-algebras
64
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A direc sum of nilpotent Lie algebras such that $C^n(\mathfrak{g}) \subsetneq \mathfrak{z}(\mathfrak{g})$

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#lie-groups #lie-algebras
287
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Haar-measure in KAK decomposition of $SL(2,\mathbb{R})$

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#measure-theory #lie-groups #lie-algebras #haar-measure
79
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Carter's construction of the Chevalley group (Case $A_1$)

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#lie-algebras #simple-groups #root-systems
431
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generators of Sp(8)

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#matrices #lie-groups #lie-algebras #symplectic-linear-algebra
270
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centralizers of nilpotent element in simple Lie algebra and associated Levi subalgebra

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#representation-theory #lie-algebras #algebraic-groups #reductive-groups
573
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Campbell-Baker-Hausdorff Theorem Proof from Stillwell

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#lie-groups #lie-algebras
870
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Fundamental, Regular, and Defining representations

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#representation-theory #lie-groups #lie-algebras

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