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Hopfish algebras

Xiang Tang·Alan Weinstein·Chenchang Zhu
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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 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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Xiang Tang, Alan Weinstein, Chenchang Zhu. 2006-04-20. Hopfish algebras. https://arxiv.org/abs/math/0510421

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