From c3d07faca536480dc86d6e60a0f7ee116a086b59 Mon Sep 17 00:00:00 2001
From: Michael Orlitzky <michael@orlitzky.com>
Date: Wed, 18 Sep 2024 18:36:48 -0400
Subject: [PATCH] {mjo-eja,examples}.tex: add the Jordan \spineja

---
 examples.tex |  5 +++++
 mjo-eja.tex  | 13 +++++++++++++
 2 files changed, 18 insertions(+)

diff --git a/examples.tex b/examples.tex
index 383cef2..09df72b 100644
--- a/examples.tex
+++ b/examples.tex
@@ -171,6 +171,11 @@
     representation and ``left multiplication by'' operator. For a
     given $x$, they are, respectively, $\quadrepr{x}$ and
     $\leftmult{x}$.
+
+    The one EJA that fits better here than anywhere else is the Jordan
+    spin algebra, $\spineja$. Its ambient space is $\Rn$, but having a
+    dedicated symbol to indicate the multiplication (which differs
+    from the componentwise multiplication on $\Rn$) is handy.
   \end{section}
 
   \begin{section}{Font}
diff --git a/mjo-eja.tex b/mjo-eja.tex
index efa68de..b9e072e 100644
--- a/mjo-eja.tex
+++ b/mjo-eja.tex
@@ -37,4 +37,17 @@
 \newcommand*{\JAut}[1]{ \operatorname{JAut}\of{{#1}} }
 
 
+% The Jordan spin algebra on R^{n}, where "n" is the first argument
+% and defaults to a literal "n".
+\newcommand*{\spineja}[1][n]{
+  \mathcal{L}^{#1}
+}
+\ifdefined\newglossaryentry
+  \newglossaryentry{spineja}{
+    name={\ensuremath{\spineja}},
+    description={the Jordan spin algebra in $n$ dimensions},
+    sort=Ln
+  }
+\fi
+
 \fi
-- 
2.44.2