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# phys documents (dragged) 78 - 72 Physics Formulary by ir....

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72 Physics Formulary by ir. J.C.A. Wevers 13.1.4 Isomorfsm and homomorfsm; representations Two groups are isomorphic if they have the same multiplication table. The mapping from group G 1 to G 2 , so that the multiplication table remains the same is a homomorphic mapping. It need not be isomorphic. A representation is a homomorphic mapping of a group to a group of square matrices with the usual matrix multiplication as the combining operation. This is symbolized by Γ . The following holds: Γ ( E )= I I, Γ ( AB )= Γ ( A ) Γ ( B ) , Γ ( A - 1 )=[ Γ ( A )] - 1 For each group there are 3 possibilities for a representation: 1. A faithful representation: all matrices are different. 2. The representation A det ( Γ ( A )) . 3. The identical representation: A 1 . An equivalent representation is obtained by performing an unitary base transformation: Γ ± ( A )= S - 1 Γ ( A ) S . 13.1.5 Reducible and irreducible representations If the same
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## This note was uploaded on 01/30/2011 for the course PHYSICS 208 taught by Professor Ye during the Spring '10 term at Blinn College.

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