Another "Missing } inserted in align* environment"

Question

I'm sorry because there are already a lot of questions on this site with such a title but no one seems to have the same problem as I have. I'm new to LaTeX and to this forum by the way. Here is my issue: without the align* environment, I get no errors, but when I want to align all my lines and use align*, I get "! Missing } inserted. } l.154 \end{align*}"

How to align all my "=" then? My code is just below. Thank you in advance for you feedback.

\begin{align*}
Ker(\psi) &= \{ (\sigma, e) \in \mathfrak A_{n} \rtimes_{\varphi} \{-1, 1\}, \psi(\sigma, e)=~$id$_{\mathfrak S_{n}} \} \\
          &= \{ (\sigma, e) \in \mathfrak A_{n} \rtimes_{\varphi} \{-1, 1\}, i(\sigma)s(e)=~$id$_{\mathfrak S_{n}} \} \\
          &= \{ (\sigma, e) \in \mathfrak A_{n} \rtimes_{\varphi} \{-1, 1\}, i(\sigma)s(e)=~$id$_{\mathfrak S_{n}} \} \\
          &= \{ (\sigma, e) \in \mathfrak A_{n} \rtimes_{\varphi} \{-1, 1\}, i(\sigma)=~$id$_{\mathfrak S_{n}}~$et$~s(e)=~$id$_{\mathfrak S_{n}} \} \\
          &= \{ ($id$_{\mathfrak A_{n}}, 1) \}
\end{align*}

Answer 1

Your problem is twofold: LaTeX giving you an error and the align environment not fulfilling your alignment needs.

The cause for the former is the use of $ characters to encapsulate what seem to be custom operators (id and Ker, I assume; as pointed out in a previous answer). The solution to this is to declare them as such with the \DeclareMathOperator macro; e.g., \DeclareMathOperator{\id}{id} for the id operator (as per the same previous answer. Note that this macro is preferred over \text and \mathrm for operators since these handle letter spacing differently.

Since you have multiple = signs on each line, to have them all line up you need to use the alignat environment (or, in your case its brother alignat*; also from the amsmath package). Using your example (with some cleanup done to your formatting to make the TeX more readable):

\documentclass{article}
\usepackage{amsmath,amsfonts,amssymb}

\DeclareMathOperator{\id}{id}
\DeclareMathOperator{\Ker}{Ker}

\begin{document}
\begin{alignat*}{3}
\Ker(\psi) &= \{(\sigma,e) \in \mathfrak{A}_n \rtimes_{\varphi} \{-1,1\}, \psi(\sigma,e) &&= \id_{\mathfrak{S}_n}\} \\
           &= \{(\sigma,e) \in \mathfrak{A}_n \rtimes_{\varphi} \{-1,1\}, i(\sigma)s(e)  &&= \id_{\mathfrak{S}_n}\} \\
           &= \{(\sigma,e) \in \mathfrak{A}_n \rtimes_{\varphi} \{-1,1\}, i(\sigma)s(e)  &&= \id_{\mathfrak{S}_n}\} \\
           &= \{(\sigma,e) \in \mathfrak{A}_n \rtimes_{\varphi} \{-1,1\}, i(\sigma)      &&= \id_{\mathfrak{S}_n} \text{et } s(e) &&= \id_{\mathfrak{S}_n}\} \\
           &= \{(\id_{\mathfrak{A}_n}, 1)\}
\end{alignat*}
\end{document}

This environment takes the number of "columns" as argument (the {3}), and the columns are separated using & characters. In this case each = sign beyond the first is preceded by a double && to achieved the desired effect.

Answer 2

The problem is not the use of align but rather the use of $ $ inside the align

Some alternatives are to use \text{id}, \mathrm{id}, or (in the preamble) \DeclareMathOperator{\id}{id}

\documentclass{article}
\usepackage{amsmath,amsfonts,amssymb}

\DeclareMathOperator{\id}{id}

\begin{document}


\begin{align*}
Ker(\psi) & = \{ (\sigma, e) \in \mathfrak{A}_n \rtimes_\varphi \{-1, 1\}, \psi(\sigma, e)=~\text{id}_{\mathfrak S_{n}} \} \\
          & = \{ (\sigma, e) \in \mathfrak{A}_{n} \rtimes_{\varphi} \{-1, 1\}, i(\sigma)s(e)=~\mathrm{id}_{\mathfrak S_{n}} \} \\
          & = \{ (\sigma, e) \in \mathfrak A_{n} \rtimes_{\varphi} \{-1, 1\}, i(\sigma)s(e)=~\id_{\mathfrak S_{n}} \} \\
          & = \{ (\sigma, e) \in \mathfrak A_{n} \rtimes_{\varphi} \{-1, 1\}, i(\sigma)=~\id_{\mathfrak S_{n}}~\text{et}~s(e)=~\id_{\mathfrak S_{n}} \} \\
          & = \{ (\id_{\mathfrak A_{n}}, 1) \}
\end{align*}
\end{document}