mjo-hurwitz.tex: new file for Hurwitz algebras (quaternions and octonions).
[mjotex.git] / mjo-eja.tex
1 %
2 % Euclidean Jordan algebras.
3 %
4 \ifx\havemjoeja\undefined
5 \def\havemjoeja{1}
6
7
8 % The jordan product of its two arguments.
9 %
10 % The choice of \circ here (as opposed to, say, \bullet) was a tough
11 % one. On the one hand, the \circ operator already means function
12 % composition, and function composition does appear in the context of
13 % (Euclidean) Jordan algebras. On the other hand, the meaning would
14 % be unambiguous to a mathematician. Perhaps more importantly -- the
15 % \circ is much easier to write on the board if one intends to teach
16 % this material. Finally, the \circ is used by Koecher, Alizadeh,
17 % Baes, Gowda, et cetera and seems to be more popular. Full
18 % disclosure: the \bullet is used by McCrimmon.
19 %
20 % It is for this reason that we have segregated the Jordan product
21 % into its own LaTeX file; we probably wouldn't want to use \circ as
22 % a (bilinear) algebra multiplication in any other context.
23 \newcommand*{\jp}[2]{{#1} \circ {#2}}
24
25
26 \fi