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.
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