Strong Symmetry Defined by Twisting Modules, Applied to Quasi-Hereditary Algebras with Triangular Decomposition and Vanishing Radical Cube

Abstract:

For a finite dimensional algebra with triangular decomposition, a new kind of modules is defined, the twisting modules. Using the structure of these modules, for some algebras with vanishing radical cube the characteristic tilting module is described and its endomorphism ring is computed. This covers both Temperley–Lieb algebras and q-Schur algebras of finite representation type. Our basic tool is a new symmetry condition, stronger than the symmetry provided by the existence of a triangular decomposition in general.