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Some representations of affine conformal transformations of Minkowski space. (English) Zbl 0927.51008

Author’s abstract: “We consider the groups \(G_1\), \(G_2\), \(G_3\) that are different from affine conformal group just because the spacelike or (and) timelike symmetries are accompanied by the inversion \(I_0\) (charge conjugation operation). For these groups there exist some fundamental spin representations (spin \(s={1\over 2}\)) given by (14) (see the paper); the representation of the subgroup formed from the proper Lorentz group, the homotheties and the considered symmetries, for different couples \(\lambda\), \(\mu\) such that \(\mu^2-\lambda^2= 1\), are equivalent”.

MSC:

51B20 Minkowski geometries in nonlinear incidence geometry
22E43 Structure and representation of the Lorentz group
53A30 Conformal differential geometry (MSC2010)
22E70 Applications of Lie groups to the sciences; explicit representations
53B50 Applications of local differential geometry to the sciences
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