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Two Constructions of Hopf Algebroids Based on the FRT Construction and Their Relations

乙戸, 勇大 北海道大学

2022.03.24

概要

We introduce two constructions of Hopf algebroids as generalizations of the FRT construction. We construct the Hopf algebroid Aσ by using a rigid family σ of elements in an arbitrary algebra L. If L is not Frobenius-separable, then this Hopf algebroid Aσ is not a weak Hopf algebra. The rigid family w of elements in an arbitrary algebra R gives birth to another Hopf algebroid U(w). The setting of this U(w) is similar to that of Hayashi's (Hopf) face algebras A(w) and of Hc(A(w)). We can show that the Hopf algebroid U(w) is a partial generalization of Aσ by constructing a strict Hopf algebroid isomorphism Φ: U(w) → Aσ.

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