Hopfish algebras

Details Hopfish algebras Hopfish algebras

2005-10-19

arxiv.org/abs/math/0510421v2

Pacific J. Math. 231 (2007), no. 1, 193--216.

Mathematics

Quantum Algebra

24 pages

Scientific paper

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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