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I would like to have a good reference where the results in

"Inclusion relations between transitive compact transformation groups" https://mathscinet.ams.org/mathscinet-getitem?mr=27:3740

can be found in English/French/Spanish.

I am particularly interested about decompositions of compact simple Lie groups. I have the translated version of the subsequent paper "Decompositions of Reductive Lie groups" where some results are mentioned, but still I am interested in the previous work.

Thanks.

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  • $\begingroup$ The three answers were useful, but Martin's was the most accessible source for me, so it got marked as accepted. $\endgroup$
    – Babs
    Commented May 11, 2018 at 18:56

3 Answers 3

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This paper was translated to English and appears in Fifteen papers on algebra. American Mathematical Society Translations. Series 2. Vol. 50; American Mathematical Society, Providence, R.I. 1966; MR189949.

This particular paper is on pages 5 to 58; Zbl 0207.33604 (and Zentralblatt entries for other papers from this book).

I did not find a copy that is freely available online, but you can see some parts in Google Books.

In case it is useful for somebody, here is also a link to the Russian original: http://mi.mathnet.ru/eng/mmo134

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Onishchik has a book "Topology of transitive transformation groups", written in English, where this material is presented in Chapter 4. The book is excellent but hard to find. I recall being unable to find it in the US and reading it in the Oberwolfach library.

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    $\begingroup$ The best math library in the US is at the University of Michigan. One should always check there if seeking hard-to-find math book in the US. I just checked, and sure enough they have it in stock (search.lib.umich.edu/catalog/record/…), so perhaps it can be obtained from there by inter-library loan. $\endgroup$
    – nfdc23
    Commented May 11, 2018 at 13:31
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if you have the Russian paper, which I do not, Google translate should do a satisfactory job; I tried it on a related paper by Onishchik, for which I do have the source: Semi-simple decompositions of semi-simple Lie algebras. A pass of the first paragraph through Google translate produces a result that seems quite workable:
I don't read Russian: no edits on my part, other than formatting.

Let $G$ be a Lie algebra, let $G'$ and $G''$ be its subalgebras, we say that the triple ($G, G', G''$) is a decomposition if $G = G' + G''$. A Lie group acting on a manifold $M$ is called locally transitive if at least one of its orbitals on $M$ is open. It is easy to see that studying decompositions of real Lie algebras is equivalent to studying the inclusion relations between locally transitive groups.
Lee transformations. If $G$ is a complex Lie algebra, $G'$ and $G''$ are its complex subalgebras, then the decomposition $(G, G', G'')$ is said to be complex. The decomposition is said to be semisimple if $G, G'$, and $G''$ are semisimple.The present paper is devoted to finding all the real and complex semisimple expansions.

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