有限维量子群的代数形式

Hopf Algebras and Quantum Groups Pub Date : 1998-08-12 DOI:10.1201/9780429187919-10

D. Nikshych, L. Vainerman

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引用次数: 16

摘要

我们建立了有限维量子群样的三个版本的等价性:由T. Yamanouchi引入的广义Kac代数，由G. Bohm, F. Nill和K. Szlachanyi引入的弱$C^*$-Hopf代数(具有对合对极)，以及由J.-M引入的Hopf双模的代数版本的Kac双模。Vallin。我们还研究了有限维量子群的结构和构造实例。

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Algebraic Versions of a Finite‐Dimensional Quantum Groupoid

We establish the equivalence of three versions of a finite dimensional quantum groupoid: a generalized Kac algebra introduced by T. Yamanouchi, a weak $C^*$-Hopf algebra introduced by G. Bohm, F. Nill and K. Szlachanyi (with an involutive antipode), and a Kac bimodule -- an algebraic version of a Hopf bimodule, the notion introduced by J.-M. Vallin. We also study the structure and construct examples of finite dimensional quantum groupoids.

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Hopf Algebras and Quantum Groups

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