documentclass{standalone}
usepackage{tikz,ifthen,xcomment,amsmath,amsfonts}
usetikzlibrary{decorations.pathmorphing,decorations.pathreplacing,arrows,automata,patterns,positioning}
newcommand{NN}{mathbb{N}}
begin{document}
 begin{align*}
     Y &= X\
 X &= left{
   tikz[scale=0.3,baseline={([yshift=-3pt]current bounding box.center)}]{
    draw[color=gray!30,fill=green](0,0) rectangle +(1,1);
   },
 right}cupbigcup_{ninNN}left{
 tikz[scale=0.3,baseline={([yshift=1pt]current bounding box.center)}]{
  draw[color=gray!30,fill=green] (0,0) rectangle (1,1);
  draw[decorate,decoration={brace}] (4,0) -- (1,0) node[midway,below=2pt] {$n$};
  },
 right}
 end{align*}

end{document}

! Missing endgroup inserted.
<inserted text>
                endgroup
l.18  end{align*}