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arXiv · 1509.03157

The Manin Hopf algebra of a Koszul Artin-Schelter regular algebra is quasi-hereditary

Theo Raedschelders·Michel Van den Bergh
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Abstract

For any Koszul Artin-Schelter regular algebra A, we consider a version of the universal Hopf algebra aut(A) coacting on A, introduced by Manin. To study the representations (i.e. finite dimensional comodules) of this Hopf algebra, we use the Tannaka-Krein formalism. Specifically, we construct an explicit combinatorial rigid monoidal category U, equipped with a functor M to finite dimensional vector spaces such that aut(A)= coend_U(M). Using this pair (U,M) we show that aut(A) is quasi-hereditary as a coalgebra and in addition is derived equivalent to the representation category of U.

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BibTeXRIS

Theo Raedschelders, Michel Van den Bergh. 2015-09-10. The Manin Hopf algebra of a Koszul Artin-Schelter regular algebra is quasi-hereditary. https://arxiv.org/abs/1509.03157

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