X-Git-Url: http://gitweb.michael.orlitzky.com/?p=mjotex.git;a=blobdiff_plain;f=mjo-eja.tex;h=b6974be8da9dff720b7817594d1b46a4d49482db;hp=0408beae0c2249f7e98ca97b326687f1ee0d9653;hb=HEAD;hpb=d4712abb88a2f342f31bbd60426d1a983df05ac2

diff --git a/mjo-eja.tex b/mjo-eja.tex
index 0408bea..efa68de 100644
--- a/mjo-eja.tex
+++ b/mjo-eja.tex
@@ -1,6 +1,9 @@
 %
 % Euclidean Jordan algebras.
 %
+\ifx\havemjoeja\undefined
+\def\havemjoeja{1}
+
 
 % The jordan product of its two arguments.
 %
@@ -18,3 +21,20 @@
 % into its own LaTeX file; we probably wouldn't want to use \circ as
 % 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