Transformation Group of the Dynamical Variables

1 Transformation Group of the Dynamical Variables. The transformation groups r(NCf) X), r(3) X and A(3) X all refer to the frame system 1 . By means of the relation between the frame and laboratory system Eq. (2.1) they may be used to define the transformations of the eulerian angles as follows  

1) with each transformation r (F) e r(3) X we may associate a basis transformation 

Key For SRMs with primitive period isometric transformations the isomorphisms hold strictly for the representations of y, jr, , r and IF, but / is homomorphic onto 

Next we consider the direct sum of the two transformation groups j/ JO and SS In the case where both these groups may be represented by linear inhomogeneous transformations according to Eqs. (2.6), (2.28) this leads to the matrix group 

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