Tuesday, March 8, 2011

so let's try to consider various "real forms" of simple complex lie algebras ...

??for example let's consider so(5) ... ???

so for example we have so(5), so(4,1), so(3,2) as real forms ... ??...

first let's consider sl(2) ... with sl(2) and su(2) as real forms .... ????....

sl(2) = rrr ??

su(2) = ???something about "pauli matrixes" ???...

01
10

0 -i
i 0

1 0
0 -1

??not at all clear that this is helping yet ... ??...

well, wait... that last one looks like it's in the cartan or something ... ???

hmm, but maybe this is suggesting that... ??the reason that macroscopic and microscopic incidence geometry doesn't survive in arbitrary real forms has to do with... ??relationship between a root and it's negative .... ???or something ...

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