Applying the q-algebras U'_q(so_n) to quantum gravity: towards q-deformed analog of SO(n) spin networks

Nonstandard q-deformed algebras U’_q(so_n), proposed a decade ago for the needs of representation theory, essentially differ from the standard Drinfeld-Jimbo quantum deformation of the algebras U(so_n) and possess with regard to the latter a number of important advantages. We discuss possible application of the q-algebras U’_q(so_n), within two different contexts of quantum/q-deformed gravity: one concerns q-deforming of D-dimensional (D >= 3) euclidean gravity, the other applies to 2+1 anti-De Sitter quantum gravity (with space surface of genus g) in the approach of Nelson and Regge.