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How can I construct the Cartan subalgebra of a semisimple Lie algebra?

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#lie-algebras #semisimple-lie-algebras
57
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An extension of an algebraic question from my test

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#linear-algebra #lie-algebras
155
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Why are these general representations of the Lorentz Lie algebra irreducible?

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#representation-theory #lie-algebras
413
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Let ‎$‎L‎$‎ be a Lie algebra. why if ‎$‎L‎$ ‎be‎ supersolvable then ‎$‎L'=[L,L]‎$ ‎ is nilpotent.‎

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#lie-algebras
379
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Prove the Weyl's complete reducibility Theorem on finite-dimensional $\mathfrak{g}-modules$ by Kostant's $\mathfrak{n}$-cohomology result

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#representation-theory #lie-algebras #homology-cohomology
164
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Root Space Decomp

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#lie-algebras
123
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Root space question

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#lie-algebras
258
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Toral sub algebra

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#lie-algebras
759
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Root space decomposition

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#linear-algebra #abstract-algebra #lie-algebras
1.1k
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How are the roots of a Lie algebra related to its Killing form?

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#linear-algebra #lie-algebras #root-systems
618
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How to visualise the Killing form of a Lie algebra

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#abstract-algebra #lie-algebras
1.4k
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killing form and the dot product

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#linear-algebra #abstract-algebra #lie-algebras #root-systems
790
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Closure of a Fundamental Weyl Chamber

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#abstract-algebra #lie-algebras #root-systems
505
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Associative Lie algebra without Jacobi identity

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#abstract-algebra #lie-algebras #associativity
133
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How are the components of a connection on a homogenous space related to the Mauer-Cartan form?

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#differential-geometry #lie-groups #lie-algebras #principal-bundles #connections

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