What is the best way to translate the mathematical term ''intertwiner'' (between two representations of a group) into German?
Intertwiner in german?
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0Personally, I don't like the word 'intertwiner'; I don't think this concept deserves a special name. I prefer G-morphism, or k[G]-linear map, or something like that (and these have obvious translations into other languages). – 2012-07-18
3 Answers
Excuse me if mine is a very low-brow approach.
Let us look at the English Wikipedia page Equivariant Maps (cf. here), where there is the definition of Interwiners, as a special kind of equivariant maps.
Then let us switch to the German version, and we find that, in the same context, it is employed just the term äquivarianten Abbildung.
I hope it helps. Bye.
Edit Added because the OP need not only tranlations but references to actual usage.
In the German literature you'll find it also in the abbreviated form $G$-Abbildung as for example here in Tammo Von Dieck's Topologie,
(In order to overcome the difficulties you report in comments, here is the exact physical reference: Chapter I, Section 10, second paragraph on page 41.)
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0From Google Books (to me the page was displayed): [40](http://i.stack.imgur.com/FtMwG.png) [41](http://i.stack.imgur.com/5wJcS.png) [42](http://i.stack.imgur.com/kKC6J.png) – 2012-07-25
The link https://mathoverflow.net/questions/46061/what-is-the-german-translation-for-intertwiner provided by Nick Kidman was quite useful. I found two old German papers by authorities in group theory
- Brauer: http://www.springerlink.com/content/g7465w3g08255142/
- Tamaschke: http://www.springerlink.com/content/t85t8k7731088573/
who use ''verkettet'' for the relationship, which suggests the name Verketter, which can indeed be found in recent lecture notes by
- Rehren: http://www.theorie.physik.uni-goettingen.de/~rehren/ps/cqft.pdf
although Rehren subsequently uses the word Intertwiner as a German Lehnswort for this concept.
Edit: p.273 of arXiv:hep-th/9805093v1 explicitly says '' intertwiners (“Verketter” in the sense of Schur)'', and Schur was probably the first one to use the concept at all. Indeed, in his paper ''Beiträge zur Theorie der Gruppen linearer homogener Substitutionen'' Trans. Amer. Math. Soc. 10 (1909), 159--175. http://www.jstor.org/stable/10.2307/1988680 , Schur uses in this context the adjective ''verkettet'', but not the substantive.
My old Technik-Wörterbuch (1982) directs me from intertwine to interlace, which it translates by verschlingen (Verschlingung, verschlungener Zyklus), which I think sounds right. These words are marked as topological terms, though, so you will have to consider if they are suitable in an algebraic context.
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0It is not enough to find possible translations; since the concept is old one also needs references for actual usage in this context. (Verschlingung sounds more like braiding, which has a very different meaning in group theory.) – 2012-07-18