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

摘要

For any Koszul Artin-Schelter regular algebra A, we consider a version of theuniversal Hopf algebra aut(A) coacting on A, introduced by Manin. To study therepresentations (i.e. finite dimensional comodules) of this Hopf algebra, weuse the Tannaka-Krein formalism. Specifically, we construct an explicitcombinatorial rigid monoidal category U, equipped with a functor M to finitedimensional 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 isderived equivalent to the representation category of U.