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.

arXiv commentV2: 27 pages, no figures. Section 3.3 on volume form completely rewritten; some minor changes. To appear in J. Noncommut. Geom