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Results tagged with lie-algebras
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user 14510
Lie algebras are algebraic structures which were introduced to study the concept of infinitesimal transformations. The term "Lie algebra" (after Sophus Lie) was introduced by Hermann Weyl in the 1930s. In older texts, the name "infinitesimal group" is used. Related mathematical concepts include Lie groups and differentiable manifolds.
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Why is Lie's Third Theorem difficult?
@Theo, doubtless in the year since you answered this question, someone who can produce such impressive notes would have gotten all the details of a thorough answer sorted out, but my own proof of Lie …
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Ado's Theorem Proof
Could someone please tell me what I am missing in the following argument. Either my understanding of the exact statement of Ado's theorem is wrong, or there is a flaw in my argument below.
For a fin …
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Is every Lie subgroup of GL(V) isomorphic to a (maybe another) closed subgroup of GL(V)?
I am gathering material for an exposition and I note that some texts (e.g. Ise and Takeuchi, "Lie Groups I & II", Stillwell, "Naive Lie Theory", Hall, "Lie Groups, Lie Algebras, and Representations") …
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When is the Ad (Adjoint Representation) Morphism a Closed Map
Given a Lie group $\mathfrak{G}$ with finite centre and with Lie algebra $\mathfrak{g}$, I am looking at a simple proof that negative definite Killing form implies compactness. This proof is given her …
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33
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3
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When is a finite dimensional real or complex Lie Group not a matrix group
I have a smattering of knowledge and disconnected facts about this question, so I would like to clarify the following discussion, and I also seek references and citations supporting this knowledge. P …
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