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arxiv: math/0510421 · v2 · pith:UJ5I2K7V · submitted 2005-10-19 · math.QA

Hopfish algebras

Xiang Tang , Alan Weinstein , Chenchang Zhu This is my paper

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keywords hopfishalgebraalgebrasstructureallowingantipodeassociativebimodules
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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 examples of hopfish algebras. We find that a hopfish structure on the commutative 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.

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