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Why is such a representation of $\mathfrak{sl}_{2}(\mathbb{C})$ irreducible?

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#representation-theory #lie-groups #lie-algebras
328
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Homeomorphic to $SO(3)$

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#group-theory #lie-groups #quaternions
466
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Exponential of operators satisfying Heisenberg Commutation Relation

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#lie-groups #lie-algebras #heisenberg-group
736
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Using coordinates to show left-invariant vector fields form Lie algebras

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#group-theory #lie-groups #mathematical-physics #invariance
78
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Examples of $e^A e^B \neq e^C $

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#matrices #lie-groups
94
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Matricial form of the killing form of $\mathfrak{sl}(n)$

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#representation-theory #lie-groups #lie-algebras
457
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Compute that the associated Lie algebra homomorphism $\mathfrak{su}(2)\rightarrow\mathfrak{so}(3) $ explicitly

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#linear-algebra #differential-geometry #lie-groups #lie-algebras
174
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I want to show that two different definitions of the adjoint representation of a Lie group are equivalent.

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#lie-groups #lie-algebras
284
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How does one show that $SO(6)/U(3)\cong \Bbb C\rm P^3$?

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#differential-topology #lie-groups #homogeneous-spaces
102
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Is every geometry contained in a maximal geometry?

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#group-theory #differential-geometry #differential-topology #lie-groups #smooth-manifolds
133
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Globalization of a Representation

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#abstract-algebra #representation-theory #lie-groups #connectedness #topological-groups
617
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How to proof the Casimir element is in the Center of U(g)

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#representation-theory #lie-groups #lie-algebras
1.2k
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Fundamental v.s. Anti-Fundamental Representation of $SU(N)$: Why special at $N=2$

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#abstract-algebra #representation-theory #lie-groups #lie-algebras
240
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Projective Spin group and Spin$^C$ groups?

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#algebraic-topology #lie-groups #projective-geometry #exact-sequence
80
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Relative invariant w.r.t. $Xf$

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#group-theory #finite-groups #lie-groups

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