We prove that every simple transitive 2-representation of the fiat 2-category of Soergel bimodules (over the coinvariant algebra) in type B2 is equivalent to a cell 2-representation. We also describe some general properties of the 2-category of Soergel bimodules for arbitrary finite Dihedral groups.

We discuss the structure of Motzkin algebra [Formula: see text] by introducing a sequence idempotents and basic construction. show that admits factor trace if only higher commutants these factors depend on text]. Then family irreducible bimodules over is constructed. A tensor category with fusion rule obtained from bimodules.

We extend to bimodules Schelter’s localization of a ring with respect to Gabriel filters of left and right ideals. Our two-sided localization of bimodules provides an endofunctor on a convenient bicategory of rings with filters of ideals. This is used to study the Picard group of a ring relative to a filter of ideals.

In 1966 [1], Auslander introduced a class of finitely generated modules having a certain complete resolution by projective modules. Then using these modules, he defined the G-dimension (G ostensibly for Gorenstein) of finitely generated modules. It seems appropriate then to call the modules of G-dimension 0 the Gorenstein projective modules. In [4], Gorenstein projective modules (whether finite...

We prove a conjecture of A. S. Buch concerning the structure constants of the Grothendieck ring of a flag variety with respect to its basis of Schubert structure sheaves. For this, we show that the coefficients in this basis of the structure sheaf of any subvariety with rational singularities, have alternating signs. Equivalently, the class of the dualizing sheaf of such a subvariety is a nonne...

Gross and Hopkins have proved that in chromatic stable homotopy, Spanier-Whitehead duality nearly coincides with Brown-Comenetz duality. Our goal is to give a conceptual interpretation for this phenomenon in terms of the Gorenstein condition for maps of ring spectra in the sense of [5] We describe a general notion of Brown-Comenetz dualizing module for a map of ring spectra and show that in thi...