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Modified traces for quasi-Hopf algebras

Abstract : Let H be a finite-dimensional unimodular pivotal quasi-Hopf algebra over a field k , and let H -mod be the pivotal tensor category of finite-dimensional H -modules. We give a bijection between left (resp. right) modified traces on the tensor ideal H -pmod of projective modules and left (resp. right) cointegrals for H . The non-zero left/right modified traces are non-degenerate, and we show that non-degenerate left/right modified traces can only exist for unimodular H . This generalises results of Beliakova, Blanchet, and Gainutdinov [1] from Hopf algebras to quasi-Hopf algebras. As an example we compute cointegrals and modified traces for the family of symplectic fermion quasi-Hopf algebras.
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https://hal.archives-ouvertes.fr/hal-02432659
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Submitted on : Wednesday, November 25, 2020 - 4:36:21 PM
Last modification on : Wednesday, January 20, 2021 - 5:56:15 AM

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Johannes Berger, Azat M. Gainutdinov, Ingo Runkel. Modified traces for quasi-Hopf algebras. J.Algebra, 2020, 548, pp.96-119. ⟨10.1016/j.jalgebra.2019.12.006⟩. ⟨hal-02432659⟩

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