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15
95
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Verma modules as representations of the Borel

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#representation-theory #lie-algebras #semisimple-lie-algebras #verma-modules
138
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Relation between generators of $\mathfrak{sl}_2(\mathbb{R})$ and $SL_2(\mathbb{R})$

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#differential-geometry #lie-groups #lie-algebras #smooth-manifolds #differential-forms
48
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Constructing a basis for $\mathfrak{su}(2)$ that spans a specific subspace

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#linear-algebra #lie-algebras
115
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How to find the Lie algebra of $G:=\{A\in GL_2(\Bbb{R}): A^tQA=Q\}$?

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#abstract-algebra #matrices #functional-analysis #analysis #lie-algebras
88
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Understanding Tangent Space under Context of Lie Theory

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#lie-groups #lie-algebras #smooth-manifolds
35
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Solvable radical and closed Lie subgroups

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#lie-groups #lie-algebras #smooth-manifolds #normal-subgroups #topological-groups
111
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What is the definition of a vector field generating a Lie group of symmetries which is not necesserally a 1-parameter group?

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#partial-differential-equations #lie-groups #lie-algebras #integrable-systems
36
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Lie algebra homomorphism induces lie group homomorphism

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#lie-groups #lie-algebras
28
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Nilpotent subalgebras and ideals

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#linear-algebra #lie-groups #lie-algebras
54
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The interpretation of Jacobi identity in terms of Lie group

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#lie-groups #lie-algebras
41
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A question on alternating product and $SL_n(R)$

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#lie-groups #lie-algebras #exterior-algebra #tangent-spaces
70
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Why universal enveloping algebra U$(\mathfrak{g})$ has the same representation theory as that of $\mathfrak{g}$?

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#lie-algebras #universal-algebra #representation-of-algebras
75
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Why $(\mathfrak g_{\mathbb C},K)$-modules?

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#number-theory #representation-theory #lie-algebras #automorphic-forms #langlands-program
36
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Universal enveloping algebra as the algebra of left-invariant differential operators

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#lie-groups #lie-algebras
172
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The group $SO(1,3)$ and its Lie algebra

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#lie-groups #lie-algebras #special-relativity

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