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

Journal Contribution - Journal Article

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.
Journal: Advances in Mathematics
ISSN: 0001-8708
Volume: 305C
Pages: 601-660
Number of pages: 60
Publication year:2015
Keywords:math.RT, math.QA, math.RA, 16S10, 16S37, 16S38, 16T05, 16T15, 20G42, Pure mathematics