From: Michael Orlitzky <michael@orlitzky.com>
Date: Thu, 19 Sep 2024 13:24:23 +0000 (-0400)
Subject: {mjo-linear_algebra,examples}.tex: add the derivations Der(V) on V
X-Git-Url: https://gitweb.michael.orlitzky.com/?a=commitdiff_plain;h=49495caafaa729f757ee4a5ff05bf14b643019f5;p=mjotex.git

{mjo-linear_algebra,examples}.tex: add the derivations Der(V) on V
---

diff --git a/examples.tex b/examples.tex
index 09df72b..9096b70 100644
--- a/examples.tex
+++ b/examples.tex
@@ -253,6 +253,9 @@
       \oplus \oplusperp \oplus \oplusperp
     \end{align*}
     \normalsize
+
+    If $V$ is an algebra, then $\Der{V}$ is the space of all
+    (linear) derivations on $V$.
   \end{section}
 
   \begin{section}{Listing}
diff --git a/mjo-linear_algebra.tex b/mjo-linear_algebra.tex
index b85a710..062121f 100644
--- a/mjo-linear_algebra.tex
+++ b/mjo-linear_algebra.tex
@@ -186,4 +186,14 @@
 \fi
 
 
+% The space of all (linear) derivations on its argument, an algebra.
+\newcommand*{\Der}[1]{\operatorname{Der}\of{#1}}
+\ifdefined\newglossaryentry
+  \newglossaryentry{Der}{
+    name={\ensuremath{\Der{V}}},
+    description={the space of all (linear) derivations on $V$},
+    sort=Der
+  }
+\fi
+
 \fi