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

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

2008-05-15

arxiv.org/abs/0805.2401v1

Mathematics

Quantum Algebra

4 pages

Scientific paper

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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