Flatness of Noetherian Hopf algebras over coideal subalgebras

Skryabin, Serge

doi:10.48550/arxiv.2001.02848

2020

DOI: 10.48550/arxiv.2001.02848

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Flatness of Noetherian Hopf algebras over coideal subalgebras

Serge Skryabin¹

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2021

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“…(i) Λ is a noetherian integral domain, (ii) the action of H on Λ extends to an action on the field of fractions L = Frac(Λ), (iii) Λ is faithful as a left module over the smash product Λ#H.Remark 2.2. (1) We regard H as part of the data which specifies H.(2) Condition (ii) holds for example if the coradical of H is finite-dimensional or cocommutative[SV06], or if H acts locally finitely on Λ[Skr20].…”

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Harish-Chandra modules over Hopf Galois orders

Hartwig¹

2021

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The theory of Galois orders was introduced by Futorny and Ovsienko [FO10]. We introduce the notion of H-Galois Λ-orders. These are certain noncommutative orders F in a smash product of the fraction field of a noetherian integral domain Λ by a Hopf algebra H (or, more generally, by a coideal subalgebra of a Hopf algebra). They are generalizations of Webster's principal flag orders [Web19]. Examples include Cherednik algebras, as well as examples from Hopf Galois theory. We also define spherical Galois orders, which are the corresponding generalizations of principal Galois orders introduced by the author [Har20].The main results are (1) for every maximal ideal m of Λ of finite codimension, there exists a simple Harish-Chandra F -module in the fiber of m; (2) for every character of Λ we construct a canonical simple Harish-Chandra module as a subquotient of the module of local distributions; (3) if a certain stabilizer coalgebra is finite-dimensional, then the corresponding fiber of simple Harish-Chandra modules is finite; (4) centralizers of symmetrizing idempotents are spherical Galois orders and every spherical Galois order appears that way.

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Harish-Chandra modules over Hopf Galois orders

Hartwig¹

2021

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Flatness of Noetherian Hopf algebras over coideal subalgebras

Cited by 1 publication

References 18 publications

Harish-Chandra modules over Hopf Galois orders

Harish-Chandra modules over Hopf Galois orders

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