What I want are the symbols used in the textbook Theory of group representations and applications of Asom O. Barut and Ryszard Raczka (2n ed.) for semidirect sum and semidirect product. I upload a photo.

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I have been looking for in Unicode symbols and i don't find anything, so probably it is going to be diffcult.


Remark. This question have been marked as possible duplicate question. I don't agree with that. I've tried to use Detexify to find my symbol, but it didn't recognize it. Probably I should study The Comprehensive LaTeX Symbol List better, but that is another question. Any of the answers provided in How to look up a symbol or identify a math symbol or character? solves my problem.


2 Answers 2


You can build the symbols yourself.





$A\roplus B\rotimes C\loplus D \lotimes E$

$\scriptstyle \roplus\rotimes\loplus\lotimes$


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However, note that the standard \oplus and \otimes are lighter than + and \times, so you may want to redefine also them in a similar way, using the full circle.


I have just found it. It is defined in stix package, as: \oplusrhrim and \otimesrhrim.

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  • Notice that many authors (ab)use the $\ltimes$ and $\rtimes$ symbols for that (mainly because issues with the interplay between stix and amsmath, see section 2.2 of the stix manual).
    – user121799
    Commented Feb 16, 2018 at 19:50
  • I thought \rtimes and \ltimes were the snatdard symbols. They aren't the usual?
    – Dog_69
    Commented Feb 16, 2018 at 20:03
  • What do you mean by "standard"? They come with a vertical bar on the either left- or right-hand side, and thus resemble your symbols, and they are widely used in the literature (even though the one you found look more like the original ones).
    – user121799
    Commented Feb 16, 2018 at 20:15
  • What I wanted to say is that I thought the ''canonical'' to denote the semidirect product was the \rtimes, for example in Wikipedia's article. And that until Barut and Raczka's book, I'd not seen these symbols. But I agree with you. From my point of view, stix's symbols seems more natural or ''correct''.
    – Dog_69
    Commented Feb 16, 2018 at 21:08

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