Articoli correlati a Triality: Vector Space, Mathematics, Duality (Mathematics),...

Triality: Vector Space, Mathematics, Duality (Mathematics), Dual Vector Space, Double Covering Group - Brossura

 
9786131140044: Triality: Vector Space, Mathematics, Duality (Mathematics), Dual Vector Space, Double Covering Group

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, triality is a relationship between three vector spaces, analogous to the duality relation between dual vector spaces. Most commonly, it describes those special features of the group Spin(8), the double cover of 8-dimensional rotation group SO(8), arising because the group has an outer automorphism of order three. There is a geometrical version of triality, analogous to duality in projective geometry. Of all simple Lie groups, Spin(8) has the most symmetrical Dynkin diagram. The diagram has four nodes with one node located at the center, and the other three attached symmetrically. The symmetry group of the diagram is the symmetric group S3 which acts by permuting the three legs. This gives rise to an S3 group of outer automorphisms of Spin(8). This automorphism group permutes the three 8-dimensional irreducible representations of Spin(8); these being the vector representation and two chiral spin representations.

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