The antipode of a dual quasi-Hopf algebra with nonzero integrals is bijective

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dc.creatorBeattie, Margaret
dc.creatorIovanov, Miodrag Cristian
dc.creatorRaianu, Serban
dc.date2008-05-15
dc.date.accessioned2026-07-07T09:39:20Z
dc.date.available2026-07-07T09:39:20Z
dc.descriptionFor $A$ a Hopf algebra of arbitrary dimension over a field $K$, it is well-known that if $A$ has nonzero integrals, or, in other words, if the coalgebra $A$ is co-Frobenius, then the space of integrals is one-dimensional and the antipode of $A$ is bijective. Bulacu and Caenepeel recently showed that if $H$ is a dual quasi-Hopf algebra with nonzero integrals, then the space of integrals is one-dimensional, and the antipode is injective. In this short note we show that the antipode is bijective.
dc.description4 pages
dc.identifierhttps://arxiv.org/abs/0805.2401
dc.identifierhttp://arxiv.org/abs/0805.2401
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/161134
dc.subjectQuantum Algebra
dc.subject16W30
dc.titleThe antipode of a dual quasi-Hopf algebra with nonzero integrals is bijective
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