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Lie Groups, Physics, and Geometry by Robert Gilmore

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12

Riemannian symmetric spaces

 

 

In the classification of the real forms of the simple Lie algebras we encountered subspaces images, iimages on which the Cartan–Killing inner product was negative-definite (on images) or positive-definite (on iimages). In both cases these subspaces exponentiate onto algebraic manifolds on which the invariant metric gij is definite, either ...

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