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Are all $\mathfrak{su}(n)$ irreducible representations faithful?

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#representation-theory #lie-algebras #semisimple-lie-algebras
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There are no semisimple Lie algebras of dimension $4$, $5$, or $7$

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#abstract-algebra #lie-algebras #root-systems #semisimple-lie-algebras
76
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Why $H$ in $\mathfrak{sl}_2$ triple is always semisimple?

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#representation-theory #lie-algebras #semisimple-lie-algebras #representation-of-algebras
730
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Why do we call adjoint Lie groups "adjoint"?

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#group-theory #terminology #lie-groups #semisimple-lie-algebras
75
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Primeness in semi-simple Lie algebra

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#abstract-algebra #lie-algebras #maximal-and-prime-ideals #semisimple-lie-algebras
146
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Involutive automorphism of simple Lie algebra

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#lie-groups #lie-algebras #semisimple-lie-algebras #involutions #symmetric-spaces
370
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Non-existence of semi-simple Lie algebras with dimension $4$ or $5$

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#lie-algebras #semisimple-lie-algebras
238
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the Cartan subalgebra and a argument of the sum of two diagonalizable endomorphisms

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#proof-explanation #lie-algebras #solution-verification #diagonalization #semisimple-lie-algebras
94
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Given a dominant algebraically integral weight, how to construct all other weights and what are their multiplicities?

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#representation-theory #semisimple-lie-algebras
67
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Prime ideals of Diamond Lie algebra

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#abstract-algebra #lie-algebras #ideals #maximal-and-prime-ideals #semisimple-lie-algebras
673
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$SO(p,q)$ Fundamental Weights?

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#representation-theory #lie-algebras #mathematical-physics #root-systems #semisimple-lie-algebras
145
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Constructing the root diagram for $B_2$

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#lie-algebras #root-systems #semisimple-lie-algebras #dynkin-diagrams
562
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Why is the realification of a simple complex Lie algebra a semisimple real Lie algebra?

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#lie-algebras #semisimple-lie-algebras
64
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Gabber's analogue of Bernstein inequality for category $\mathcal{O}$

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#reference-request #lie-algebras #algebraic-groups #semisimple-lie-algebras #dimension-theory-algebra
199
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Every Lie algebra endomorphism of $\mathfrak{so}(3)$ is given by the anticommutator with a symmetric matrix.

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#matrices #lie-algebras #symmetric-matrices #semisimple-lie-algebras

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