Abstract
It is known that a dual quasi-bialgebra with antipode H, i.e., a dual quasi-Hopf algebra, fulfils a fundamental theorem for right dual quasi-Hopf H-bicomodules. The converse in general is not true. We prove that, for a dual quasi-bialgebra H, the structure theorem is equivalent to the existence of a suitable map S: H → H that we call a preantipode of H.
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This paper was written while the first author was a member of GNSAGA and both authors were partially supported by MIUR within the National Research Project PRIN 2007. Part of the paper is included in the master degree thesis of the second author which was developed under the supervision of the first author.
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Ardizzoni, A., Pavarin, A. Preantipodes for dual quasi-bialgebras. Isr. J. Math. 192, 281–295 (2012). https://doi.org/10.1007/s11856-012-0024-1
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DOI: https://doi.org/10.1007/s11856-012-0024-1