JournalsjncgVol. 12, No. 4pp. 1469–1501

A class of differential quadratic algebras and their symmetries

  • Giovanni Landi

    Università di Trieste, Italy
  • Chiara Pagani

    Universität Göttingen, Germany and INDAM - GNSAGA, Italy
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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.

Cite this article

Giovanni Landi, Chiara Pagani, A class of differential quadratic algebras and their symmetries. J. Noncommut. Geom. 12 (2018), no. 4, pp. 1469–1501

DOI 10.4171/JNCG/313