X-Git-Url: http://gitweb.michael.orlitzky.com/?p=mjotex.git;a=blobdiff_plain;f=mjo-eja.tex;fp=mjo-eja.tex;h=0408beae0c2249f7e98ca97b326687f1ee0d9653;hp=0000000000000000000000000000000000000000;hb=d4712abb88a2f342f31bbd60426d1a983df05ac2;hpb=cd69cb906bece22ab124082f723cc08d460b7f83 diff --git a/mjo-eja.tex b/mjo-eja.tex new file mode 100644 index 0000000..0408bea --- /dev/null +++ b/mjo-eja.tex @@ -0,0 +1,20 @@ +% +% Euclidean Jordan algebras. +% + +% The jordan product of its two arguments. +% +% The choice of \circ here (as opposed to, say, \bullet) was a tough +% one. On the one hand, the \circ operator already means function +% composition, and function composition does appear in the context of +% (Euclidean) Jordan algebras. On the other hand, the meaning would +% be unambiguous to a mathematician. Perhaps more importantly -- the +% \circ is much easier to write on the board if one intends to teach +% this material. Finally, the \circ is used by Koecher, Alizadeh, +% Baes, Gowda, et cetera and seems to be more popular. Full +% disclosure: the \bullet is used by McCrimmon. +% +% It is for this reason that we have segregated the Jordan product +% 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}}