List questions from lie-algebras

Published on 11 Apr 2026 - 6:44

24

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Find basis $\beta$ of $M$ such that $\phi(H)$ sits inside diagonal matrices, $\phi(S)$ sits inside upper triangular matrices w.r.t. basis $\beta$

Published on 01 May 2026 - 8:21

227

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Why do linear splitting maps of Lie Algebra central extensions induce cocycles?

Published on 25 Apr 2026 - 23:51

216

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Coadjoint representation $Ad^*$ of the Heisenberg group

Published on 16 Apr 2026 - 1:31

961

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Express fundamental coweights using coroots.

Published on 10 Apr 2026 - 16:20

24

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How to show that $( \Lambda^3 g)^{g} = \mathbb{C}Z$?

Published on 14 Apr 2026 - 8:38

53

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Finite dimensional representation of $SL_{2}$

Published on 17 Apr 2026 - 12:31

227

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Identity for bracket operator in tangent space at identity

Published on 11 Apr 2026 - 0:10

337

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Flows and Lie brackets, $\beta$ not a priori smooth at $t = 0$

Published on 26 Apr 2026 - 0:33

503

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Poisson bracket makes $C^\infty(M)$ into a Lie algebra

Published on 29 Mar 2026 - 17:31

337

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Lie group homomorphism with injective Lie algebra homomorphism

Published on 15 Apr 2026 - 2:56

114

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Different methods to compute a unitary representation

Published on 12 Apr 2026 - 15:45

1.1k

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A tensor identity - $\text{Hom}_{R}(A,B \otimes_S C) \cong \text{Hom}_{R}(A,B)\otimes _SC$

Published on 16 Apr 2026 - 15:52

165

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Complexification of maximal compact subgroup of $GL(2,\mathbb{R})$.

Published on 12 Apr 2026 - 15:26

109

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Abelian subalgebra doesn't imply toral

Published on 16 Apr 2026 - 15:53

List Question

The inner product on $\mathfrak{h}^*$ induced by the inner product on $\mathfrak{h}$.

Find basis $\beta$ of $M$ such that $\phi(H)$ sits inside diagonal matrices, $\phi(S)$ sits inside upper triangular matrices w.r.t. basis $\beta$

Why do linear splitting maps of Lie Algebra central extensions induce cocycles?

Coadjoint representation $Ad^*$ of the Heisenberg group

Express fundamental coweights using coroots.

How to show that $( \Lambda^3 g)^{g} = \mathbb{C}Z$?

Finite dimensional representation of $SL_{2}$

Identity for bracket operator in tangent space at identity

Flows and Lie brackets, $\beta$ not a priori smooth at $t = 0$

Poisson bracket makes $C^\infty(M)$ into a Lie algebra

Lie group homomorphism with injective Lie algebra homomorphism

Different methods to compute a unitary representation

A tensor identity - $\text{Hom}_{R}(A,B \otimes_S C) \cong \text{Hom}_{R}(A,B)\otimes _SC$

Complexification of maximal compact subgroup of $GL(2,\mathbb{R})$.

Abelian subalgebra doesn't imply toral

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