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Lapidus
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Anybody here how could explain to me in the simplest terms triality?
I know some very littel Lie and representation theory. As I understand there are vector and spinor representations for so(n). If n is even, there are two spin reps and one vec rep, if n is odd there is one spin rep and one vec rep.
For example, for n=4 there are the two 2-dim Weyl spinors and the one 4-dim vec representation.
so(8) is special, since the dim of the two spin reps and the one vec rep is ithe same, 8.
Now, how do these two spinors look for so(8)?
They say triality gives the symmetry of Spin(8), not of so(8), it is an automorphism of Spin(8). What does that mean?
I asked the question here, not in the math section, because most of the time I do not understand mathematicans when they talk about Lie algebras and representations...
thank you
I know some very littel Lie and representation theory. As I understand there are vector and spinor representations for so(n). If n is even, there are two spin reps and one vec rep, if n is odd there is one spin rep and one vec rep.
For example, for n=4 there are the two 2-dim Weyl spinors and the one 4-dim vec representation.
so(8) is special, since the dim of the two spin reps and the one vec rep is ithe same, 8.
Now, how do these two spinors look for so(8)?
They say triality gives the symmetry of Spin(8), not of so(8), it is an automorphism of Spin(8). What does that mean?
I asked the question here, not in the math section, because most of the time I do not understand mathematicans when they talk about Lie algebras and representations...
thank you