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diff --git a/mjo-eja.tex b/mjo-eja.tex
index b6974be..efa68de 100644
--- a/mjo-eja.tex
+++ b/mjo-eja.tex
@@ -22,5 +22,19 @@
 % a (bilinear) algebra multiplication in any other context.
 \newcommand*{\jp}[2]{{#1} \circ {#2}}
 
+% The "quadratic representation" of the ambient space applied to its
+% argument. We have standardized on the "P" used by Faraut and Korányi
+% rather than the "U" made popular by Jacobson.
+\newcommand*{\quadrepr}[1]{P_{#1}}
+
+% The "left multiplication by" operator. Takes one argument, the thing
+% to multiply on the left by. This has meaning more generally than in
+% an EJA, but an EJA is where I use it.
+\newcommand*{\leftmult}[1]{L_{#1}}
+
+% The ``Jordan automorphism group of'' operator. Using
+% \Aut{} is too ambiguous sometimes.
+\newcommand*{\JAut}[1]{ \operatorname{JAut}\of{{#1}} }
+
 
 \fi