Title: A class of differential quadratic algebras and their symmetries,
Abstract: 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. We determine
quantum groups of symmetries for the general algebras and construct
finite-dimensional covariant differential calculi.