TILTING THEORY FOR QUIVERS AND RELATED CATEGORIES MORITZ GROTH AND JAN ŠŤOVÍČEK Abstract. We generalize the construction of reflection functors from classical representation theory of quivers to arbitrary small categories with freely attached sinks or sources. These reflection morphisms are shown to induce equivalences between the corresponding representation theories with values in arbitrary s...

Owing to the difference in K-theory, an example by Dugger and Shipley implies that equivalence of stable categories Gorenstein projective modules should not be a Quillen equivalence. We give sufficient necessary condition for Frobenius pair faithful functors between two abelian equivalence, which is also equivalent induce mutually inverse equivalences objects. show category objects Waldhausen c...

We shall show that every stable equivalence (functor) between representation-finite selfinjective algebras not of type (D3m, s/3, 1) with m ≥ 2, 3 s lifts to a standard derived equivalence. This implies that all stable equivalences between these algebras are of Morita type.

We investigate Khovanov homology of stable equivalence classes of link diagrams on oriented surfaces. We apply Bar-Natan’s geometric formalism to this setting and using unoriented 1+1-dimensional topological quantum field theories we define new link homology theories for stable equivalences classes.

We present a novel notion of stable objects in a triangulated category. This Postnikov-stability is preserved by equivalences. We show that for the derived category of a projective variety this notion includes the case of semistable sheaves. As one application we compactify a moduli space of stable bundles using genuine complexes via Fourier-Mukai transforms. MSC 2000: 14F05, 14J60, 14D20

Abstract. By using cutting strips and transformations on outside decompositions of a skew diagram, we show that the Giambelli type matrices of a skew Schur function are stably equivalent to each other over symmetric functions. As a consequence, the Jacobi-Trudi matrix and the dual Jacobi-Trudi matrix are stably equivalent over symmetric functions. This gives an affirmative answer to an open pro...

We investigate when an exact functor F ∼= − ⊗Λ MΓ : mod-Λ → mod-Γ which induces a stable equivalence is part of a stable equivalence of Morita type. If Λ and Γ are finite dimensional algebras over a field k whose semisimple quotients are separable, we give a necessary and sufficient condition for this to be the case. This generalizes a result of Rickard’s for self-injective algebras. As a corol...