Tagged Questions

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Considerations for moving a function inside or outside of an integral

Excluding the possibility that $A(t)$ is the limit of a sequence, are there any special considerations I should be concerned with regarding the following assertion: Let $A(t)$ be an $n\times n$ ...
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I'm looking for list of identities involving adjoint action $\mathrm{ad}_A X = [A,X] = AX - XA$. For example, it can be easily shown that: e^{\mathrm{ad}_A} X = e^A X e^{-A} ...
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Lie rings: reference request

Dear friends: I am looking for a modern reference for Lie rings (In particular, I would like to have nice references for the structure of Lie ideals), let it be lecture notes or a book, in the sense ...
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Does an ideal of finite codimension in a finitely generated algebra have always to be finitely generated?

I have been reading a book on Lie Algebras ("Álgebras de Lie" by San Martin) and there is this exercise in the chapter on universal enveloping algebras with a claim that I can not prove: Suppose ...
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Infinite series of nested commutators

I'm trying to show the following: If $S_i$ are a set of three matrices such that $$[S_i, S_j] = \epsilon_{ijk} S_k$$ then $$\exp\big( \alpha_i [S_i, \cdot]\big) S_j = (\exp (M) \vec{S})_j$$ ...