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Flatness over PI coideal subalgebras

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Abstract

Under the assumption that a residually finite-dimensional Hopf algebra H has an Artinian ring of fractions, it is proved that H is a flat module over any right coideal subalgebra satisfying a polynomial identity and is faithfully flat over any polynomial identity Hopf subalgebra. As a consequence we find a large class of Hopf algebras which are flat over all coideal subalgebras and are faithfully flat over all Hopf subalgebras.

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Authors and Affiliations

  1. Institute of Mathematics and Mechanics, Kazan Federal University, Kremlevskaya St. 18, 420008, Kazan, Russia

    Serge Skryabin

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  1. Serge Skryabin
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Correspondence to Serge Skryabin.

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Skryabin, S. Flatness over PI coideal subalgebras. Isr. J. Math. 245, 735–772 (2021). https://doi.org/10.1007/s11856-021-2225-y

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  • DOI: https://doi.org/10.1007/s11856-021-2225-y

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