Supercoherent states, simplest supergroups and associated supergeometries

In this paper, geometries and supergeometries are analyzed from the point of view of the coset coherent states. To this end, before detailing the different factorizations of the simplest cosets, the dynamics and structure of Supercoherent states of the Klauder–Perelomov type (that are defined taking into account the geometry of the coset based on the simplest supergroup [Formula: see text] in the context of extensions of the standard model that were given previously in [A. B. Arbuzov and D. J. Cirilo-Lombardo, Phys. Scr. 94 (2019) 125302] as structural basis of the electroweak sector of the standard model (SM)) are used. The supergeometrical descriptions with such coherent superstates which uses group representation from [Y. Ne’eman, S. Sternberg and D. Fairlie, Phys. Rept. 406 (2005) 303–377] for a beyond SM model, are also defined for the noncompact case [Formula: see text]