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 endomorphism of H that we call a preantipode of H.

Preantipodes for dual quasi-bialgebras

ARDIZZONI, Alessandro;
2012-01-01

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 endomorphism of H that we call a preantipode of H.
2012
192
1
281
295
http://arxiv.org/pdf/1012.1956.pdf
http://dx.doi.org/10.1007/s11856-012-0024-1
Dual quasi-bialgebras; structure theorem; preantipode; right dual quasi-Hopf bicomodules.
A. ARDIZZONI; A. PAVARIN
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/93437
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