[Tex/LaTex] Partial tensor product sign

math-modemath-operatorssymbolstensor

There is an asymmetric tensor-like binary product operation on rings, and the notation for it is informed by both the notation for semi-direct product \rtimes and that for tensor product \otimes. It looks like a tensor product, with the arc of the surrounding "O" missing between the lower-left leg and upper-left legs of the central "X". Here is a photo of the symbol in context, hand-drawn using an iPad:

Handwritten math notation, including the symbol I would like to replicate. The LaTeX code would be $\widehat{H}_c \rtensor \mathbb{C}[\Gamma(c)]$, if I can create a \rtensor command.

As far as I know it is so far exclusively handwritten. How can I create a glyph for this operation in LaTeX? I'd like to call it \rtensor. I have the sense that the easiest way to do this is to somehow modify the glyph for \otimes by removing an arc from one side, since I want it to be the same size and have the same spacing properties. But I don't know how to proceed.

Can someone help me typeset this symbol?

Best Answer

Here is an easy "design-your-own" TikZ solution.

enter image description here

Advantages: Easy. Nicer corners compared to clipping.

Disadvantage: Not truly the exact spacing of \otimes. But close.

Code:

\documentclass{article}
\usepackage{tikz,scalerel}

\newcommand{\rtensor}{\mathbin{\mkern1mu\scalerel*{\tikz[line width=.25]{
    \clip(0,0) circle[radius=1mm+.125pt];
    \draw(-45:.1)--(135:.1) arc (135:-135:.1) -- (45:.1);
    }}{\otimes}\mkern1mu}}

\begin{document}

$H\rtensor C_{H\rtensor C_{H\rtensor C}}$

\end{document}

Update: If it's important to get the spacing for \rtensor to be exactly the same as \otimes, you can redefine \otimes. Use \let to retain the original \otimes definition if you wish.

\documentclass{article}
\usepackage{tikz,scalerel}

\let\oldtimes\otimes

\renewcommand{\otimes}{\mathbin{\mkern1mu\scalerel*{\tikz[line width=.25]{
    \clip(0,0) circle[radius=1mm+.125pt];
    \draw(0,0) circle[radius=.1]; \draw (-135:.1) -- (45:.1); \draw (135:.1) -- (-45:.1);
    }}{\oldtimes}\mkern1mu}}

\newcommand{\rtensor}{\mathbin{\mkern1mu\scalerel*{\tikz[line width=.25]{
    \clip(0,0) circle[radius=1mm+.125pt];
    \draw(-45:.1)--(135:.1) arc (135:-135:.1) -- (45:.1);
    }}{\oldtimes}\mkern1mu}}

\begin{document}

$H\rtensor C_{H\rtensor C_{H\rtensor C}}$

$H\otimes C_{H\otimes C_{H\otimes C}}$

\end{document}

enter image description here

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