Ringel duality for certain strongly quasi-hereditary algebras

Koszul Duality for Stratified Algebras I. Quasi-hereditary Algebras

We give a complete picture of the interaction between Koszul and Ringel dualities for quasi-hereditary algebras admitting linear tilting (co)resolutions of standard and costandard modules. We show that such algebras are Koszul, that the class of these algebras is closed with respect to both dualities and that on this class these two dualities commute. All arguments reduce to short computations ...

On Ringel-hall Algebras of Tame Hereditary Algebras

Based Algebras and Standard Bases for Quasi-hereditary Algebras

Quasi-hereditary algebras can be viewed as a Lie theory approach to the theory of finite dimensional algebras. Motivated by the existence of certain nice bases for representations of semisimple Lie algebras and algebraic groups, we will construct in this paper nice bases for (split) quasi-hereditary algebras and characterize them using these bases. We first introduce the notion of a standardly ...

Idempotent Subquotients of Symmetric Quasi-hereditary Algebras

We show how any finite-dimensional algebra can be realized as an idempotent subquotient of some symmetric quasihereditary algebra. In the special case of rigid symmetric algebras, we show that they can be realized as centralizer subalgebras of symmetric quasi-hereditary algebras. We also show that the infinite-dimensional symmetric quasi-hereditary algebras we construct admit quasi-hereditary s...

Smash Products of Quasi-hereditary Graded Algebras

The Smash product of a finite dimensional quasi-hereditary algebra graded by a finite group with the group is proved to be a quasihereditary algebra. Some elementary relations between the good modules of the two quasi-hereditary algebras are given.