Some construction of bicovariant differential calculi on weak Hopf algebras

Abstract

Let H be a weak Hopf algebra with an idempotent element p. Denote by H_p some twisted weak Hopf algebra associated with a generalized Drinfeld twist $(\Theta ,\overline{\Theta },p)$. Let $(\Gamma ,d)$ be a bicovariant differential calculus on H. We give some method to construct a bicovariant differential calculus $\Gamma \prime$ on H_p by a generalized Drinfeld twist, where $\Gamma \prime$ is some subspace of Γ determined by $(\Theta ,\overline{\Theta },p)$. As an application, we present some examples of bicovariant differential calculi on some face algebra and its quantum double.

Keywords:

• Bicovariant differential calculi
• face algebras
• quantum groupoids
• weak Hopf algebra

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 16T05
• 16K50

Additional information

Funding

This work was partially supported by the Fundamental Research Funds for the Central Universities under grant no. KYZ201649, the National Natural Science Foundation of China (nos. 11775116 and 11601231), and Scientific Research Foundation for Advanced Talents of Nanjing Forestry University (no. GXL011).