Vol. 231, No. 1, 2007

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 243: 1  2
Vol. 242: 1  2
Vol. 241: 1  2
Vol. 240: 1  2
Vol. 239: 1  2
Vol. 238: 1  2
Vol. 237: 1  2
Vol. 236: 1  2
Online Archive
Volume:
Issue:
     
Volumes 1–176are stored at Project Euclid
The Journal
Cover Page
Editorial Board
How To
Submissions Guidelines
Submissions Page
Subscriptions
Elect. License Agreement
Test your IP address
Contacts
To Appear

Hopfish algebras

Xiang Tang, Alan Weinstein and Chenchang Zhu

Vol. 231 (2007), No. 1, 193–216
Abstract

We introduce a notion of “hopfish algebra” structure on an associative algebra, allowing the structure morphisms (coproduct, counit, antipode) to be bimodules rather than algebra homomorphisms. We prove that quasi-Hopf algebras are hopfish algebras. We find that a hopfish structure on the algebra of functions on a finite set G is closely related to a “hypergroupoid” structure on G. The Morita theory of hopfish algebras is also discussed.

Keywords

Hopf algebra, hopfish algebra, groupoid, bimodule, Morita equivalence, hypergroupoid

Mathematical Subject Classification

Primary: 16W30

Secondary: 81R50

Milestones

Received: 2 November 2005
Accepted: 10 April 2006

Authors
Xiang Tang
Department of Mathematics
Washington University
St. Louis, MO 63130
United States
Alan Weinstein
Department of Mathematics
University of California
Berkeley, CA 94720
United States
Chenchang Zhu
Institut Fourier
Université Joseph Fourier Grenoble I
100, rue des Maths - BP 74
38402 Saint Martin d’Hères Cedex
France