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Are all closed subgroups of $\mathrm{U}(n)$ given by polynomials?

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#algebraic-geometry #lie-groups #lie-algebras
1.1k
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Definition of external Lie algebra semidirect sum

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#lie-algebras
1.2k
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Different ways of seeing how $\text{SL}(2, \mathbb{R})$ is not simply connected?

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#real-analysis #matrices #algebraic-topology #lie-groups #lie-algebras
49
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Algebraic subalgebras

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#algebraic-geometry #lie-groups #lie-algebras
51
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A commutes with everything that commutes with B

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#linear-algebra #representation-theory #lie-algebras #linear-transformations
1.1k
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Bijection from Skew-Symmetric Matrices to Orthogonal Group

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#linear-algebra #differential-geometry #lie-groups #lie-algebras
1.2k
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What is the adjoint orbit of element of lie algebra?

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#differential-geometry #lie-groups #lie-algebras
81
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What is $Z$ such that $e^X e^Y e^{-X}=e^Z $?

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#matrices #differential-geometry #exponential-function #lie-groups #lie-algebras
787
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How can we apply the exponential map to an element of a Lie group?

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#lie-groups #lie-algebras
24
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References concerning $\mathbb{C}[\partial]$-modules?

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#reference-request #lie-algebras
57
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What is the name of the theorem that says that ${\frak{g}} \subseteq \{X \in M_n(R) \mid \forall t \in R : e^{tX} \in G\}$?

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#differential-geometry #terminology #lie-groups #lie-algebras
1.3k
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Showing that the exponential map is a smooth diffeomorphism

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#linear-algebra #multivariable-calculus #differential-geometry #lie-algebras
464
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Unique dimension of Cartan subalgebras?

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#lie-algebras #associativity
300
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Simple question for matrix lie groups

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#lie-groups #lie-algebras
211
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Conditions on $\beta$ under which the trace pairing restricted to $\mathfrak{so}(V,\beta)$ is positive (negative) definite.

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#lie-groups #lie-algebras #trace #bilinear-form #trace-map

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