Koszul dual 2-functors and extension algebras of simple modules for GL2GL_2

Let p be a prime number. We compute the Yoneda extension algebra of $GL_2$ over an algebraically closed field of characteristic p by developing a theory of Koszul duality for a certain class of 2-functors, one of which controls the category of rational representations of $GL_2$ over such a field.Comment: 39 pages, title changed in second version, to appear in Selecta Math. (N.S.

Isotypic faithful 2-representations of J-simple fiat 2-categories

We introduce the class of isotypic 2-representations for finitary 2-categories and the notion of inflation of 2-representations. Under some natural assumptions we show that isotypic 2-representations are equivalent to inflations of cell 2-representations

ON AUSLANDER-REITEN TRANSLATES IN FUNCTORIALLY FINITE SUBCATEGORIES AND APPLICATIONS

Functorially finite subcategories in module categories over Artin algebras have been introduced by Auslander and Smalø [2] to provide a convenient setting for existence of relative Auslander-Reiten sequences in subcategories. Given a functorially finite subcategory, it is generally not well understood how t

On the Representation Dimension of Schur Algebras

Lower bounds for the representation dimension of Schur algebras for GL n in characteristic p?=?2n?-?1 are established. In particular it is shown that for fixed n the representation dimensions of the Schur algebras get arbitrarily large