A class of differential quadratic algebras and their symmetries

We study a multi-parametric family of quadratic algebras in four generators, which includes coordinate algebras of noncommutative four-planes and, as quotient algebras, noncommutative three-spheres. Particular subfamilies comprise Sklyanin algebras and Connes--Dubois-Violette planes.cWe determine quantum groups of symmetries for the general algebras and construct finite-dimensional covariant differential calculi.