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arXiv · 0805.2401

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

Margaret Beattie·Miodrag Cristian Iovanov·Serban Raianu
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Abstract

For $A$ 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.

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Margaret Beattie, Miodrag Cristian Iovanov, Serban Raianu. 2008-05-15. The antipode of a dual quasi-Hopf algebra with nonzero integrals is bijective. https://arxiv.org/abs/0805.2401

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