Generalized quantum phase spaces for the κ-deformed extended Snyder model

We describe, in an algebraic way, the $\kappa$-deformed extended Snyder models, that depend on three parameters $\beta, \kappa$ and $\lambda$, which a suitable algebra basis are described by de Sitter algebras ${o}(1,N)$. The commutation relations of contain parameter is used for calculations perturbative expansions. For such models we consider Heisenberg double with dual generalized momenta sector, provide respective quantum phase space depending mentioned above. Further, study these alternative double, functions group. In both cases calculate formulae cross between coordinate sectors, at linear order $\lambda$. demonstrate commutators space-time coordinates quantum-deformed terms generated $\kappa$-deformation dominating over $\beta$-dependent ones small values