mjo-eja.tex: new file for Euclidean Jordan algebras.

[mjotex.git] / mjo-eja.tex

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+%
+% 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}}