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Hopfish algebras
Xiang Tang, Alan Weinstein and Chenchang Zhu |
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Vol. 231 (2007), No. 1, 193–216
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Abstract |
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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
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Mathematical Subject Classification 2000
Primary: 16W30
Secondary: 81R50
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Milestones
Received: 2 November 2005
Accepted: 10 April 2006
Published: 1 May 2007
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Authors |
| Xiang Tang | |
| Department of Mathematics Washington University St. Louis, MO 63130 United States |
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| Alan Weinstein | |
| Department of Mathematics University of California Berkeley, CA 94720 United States |
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| Chenchang Zhu | |
| Institut Fourier Université Joseph Fourier Grenoble I 100, rue des Maths - BP 74 38402 Saint Martin d’Hères Cedex France |
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