Rafał Bocian

Weakly symmetric algebras of Euclidean type

Abstract A finite dimensional algebra A over an algebraically closed field is called a selfinjective algebra of Euclidean type if A is the orbit algebra B̂∣G, where B̂ is the repetitive algebra of a tilted algebra B of Euclidean type and G is an admissible group of automorphisms of B̂. It is known that the class of selfinjective algebras of Euclidean type coincides with the class of tame selfinjective algebras having simply connected Galois coverings and a finite (nonempty) family of generic modules. We classify all weakly symmetric algebras of Euclidean type.

The representation dimension of domestic weakly symmetric algebras

Auslander’s representation dimension measures how far a finite dimensional algebra is away from being of finite representation type. In [1], M. Auslander proved that a finite dimensional algebra A is of finite representation type if and only if the representation dimension of A is at most 2. Recently, R. Rouquier proved that there are finite dimensional algebras of an arbitrarily large finite representation dimension. One of the exciting open problems is to show that all finite dimensional algebras of tame representation type have representation dimension at most 3. We prove that this is true for all domestic weakly symmetric algebras over algebraically closed fields having simply connected Galois coverings.

Socle Deformations of Selfinjective Algebras of Euclidean Type

We classify all selfinjective finite dimensional algebras over an algebraically closed field which are socle equivalent to the selfinjective algebras of Euclidean type. In particular, nonstandard domestic selfinjective algebras in any characteristic of the base field are exhibited.

OpenMP as an Efficient Method to Parallelize Code with Dense Synchronization

In recent years, adding new cores and new threads are main methods to add computational power. In line with this approach in this paper we analyze the efficiency of the parallel computational model with shared memory, when dense synchronization is required. As our experimental evaluation shows, contemporary CPUs assisted with OpenMP library perform well in case of such tasks. We also present evidence that OpenMP is easy to learn and use.