3
\begin{align*} 
&\mathbb Q \times \{2\}&&\\
&\\
&U_{\alpha e} &&\alpha\in I_2 \text{ and }e<2 \\
&\\
&U_{\alpha 0 0} \\
&U_{\alpha 1 0} \cup U_{\alpha 0 1} \cup U_{\alpha 0 2}&&\alpha\in I_0\\
&U_{\alpha 1 0} \cup U_{\alpha 1 1} \cup U_{\alpha 1 2}
\end{align*}

produces this:

enter image description here

I want to have a curly right brace between the two columns at the bottom, indicating that $\alpha\in I_0$ is for all three bottom rows.

1

One could stack those three blocks...

\documentclass{article}
\usepackage{amsmath,amssymb,stackengine}
\setstackEOL{\#}
\setstackgap{L}{1.1\baselineskip}
\stackMath
\begin{document}
\begin{align*} 
&\mathbb Q \times \{2\}&&\\
&\\
&U_{\alpha e} &&\alpha\in I_2 \text{ and }e<2 \\
&\\
&\left.\!\!\Centerstack[l]{
U_{\alpha 0 0} \#
U_{\alpha 1 0} \cup U_{\alpha 0 1} \cup U_{\alpha 0 2}\#
U_{\alpha 1 0} \cup U_{\alpha 1 1} \cup U_{\alpha 1 2}
}
\right\}&&\alpha\in I_0\\
\end{align*}
\end{document}

enter image description here

1

Just for completeness, here's an answer that preserves the align* environment used in the OP's example. It uses an array environment to group the final three lines and to provide a closing curly brace.

enter image description here

\documentclass{article}
\usepackage{amsmath,amssymb}
\begin{document}
\renewcommand\arraystretch{1.33}

\begin{align*} 
&\mathbb Q \times \{2\}\\[1ex]
&U_{\alpha e} 
    &&\text{$\alpha\in I_2$ and $e<2$} \\[1ex]
&\mkern-5mu
\left.\begin{array}{@{}l}
U_{\alpha 0 0} \\
U_{\alpha 1 0} \cup U_{\alpha 0 1} \cup U_{\alpha 0 2}\\
U_{\alpha 1 0} \cup U_{\alpha 1 1} \cup U_{\alpha 1 2}
\end{array}\right\} 
    &&\alpha\in I_0
\end{align*}
\end{document}

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