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
--
2.45.3