\documentclass[tikz,border=10pt]{standalone}
\usepackage{mathtools}
\usetikzlibrary{braids}

\begin{document}
\begin{tikzpicture}[scale=0.4, every node/.style={scale=0.4}]
\pic[
  rotate=90,
  line width=1.5pt,
  braid/control factor=0,
  braid/nudge factor=0,
  braid/gap=0.11,
  braid/number of strands = 4,
  name prefix=braid,
] at (-0.25,0) {braid={
11111
}};
\draw[dashed,draw=black, very thick, fill=white] (1-0.5,0-0.25) rectangle ++(4,3.5);
\node at (2.5,1.5) {\fontsize{40pt}{\baselineskip}\selectfont $\alpha$};
\node at (6,1.5) {\fontsize{40pt}{\baselineskip}\selectfont $\ast$};
\pic[
  rotate=90,
  line width=1.5pt,
  braid/control factor=0,
  braid/nudge factor=0,
  braid/gap=0.11,
  braid/number of strands = 4,
  name prefix=braid,
] at (7-0.25,0) {braid={
11111
}};
\draw[dashed,draw=black, very thick, fill=white] (8-0.5,0-0.25) rectangle ++(4,3.5);
\node at (9.5,1.5) {\fontsize{40pt}{\baselineskip}\selectfont $\beta$};
\node at (13.5,1.5) {\fontsize{40pt}{\baselineskip}\selectfont $\vcentcolon=$};
\pic[
  rotate=90,
  line width=1.5pt,
  braid/control factor=0,
  braid/nudge factor=0,
  braid/gap=0.11,
  braid/number of strands = 4,
  name prefix=braid,
] at (15-0.25,0) {braid={
111
111
}};
\draw[dashed,draw=black, very thick, fill=white] (16-0.5,0-0.25) rectangle ++(2,3.5);
\node at (16.5,1.5) {\fontsize{40pt}{\baselineskip}\selectfont $\alpha$};
\draw[dashed,draw=black, very thick, fill=white] (19-0.5,0-0.25) rectangle ++(2,3.5);
\node at (19.5,1.5) {\fontsize{40pt}{\baselineskip}\selectfont $\beta$};
\end{tikzpicture}
\end{document}