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.
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Keywords
Hopf algebra, hopfish algebra, groupoid, bimodule, Morita equivalence, hypergroupoid
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Mathematical Subject Classification
Primary: 16W30
Secondary: 81R50
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Authors
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