6 papers
On Krull-Gabriel dimension of weighted surface algebras
Karin Erdmann, Alicja Jaworska-Pastuszak, Grzegorz Pastuszak
We determine the Krull-Gabriel dimension of weighted surface algebras, a class of algebras which recently appeared in the context of classification of tame symmetric periodic algeb…
On covering theory and its applications
Grzegorz Pastuszak
The aim of this survey is to present applications of covering techniques in the theory of Krull-Gabriel dimension. We start with recalling fundamental facts of the classical coveri…
Covering theory, functor categories and the Krull-Gabriel dimension
Grzegorz Pastuszak
Assume that is an algebraically closed field, a locally bounded -category, an admissible group of -linear automorphisms of and the Galois $…
On one-parameter families of hermiticity-preserving superoperators which are not positive
Grzegorz Pastuszak, Alicja Jaworska-Pastuszak, Takeo Kamizawa +1
A one-parameter family of hermiticity-preserving superoperators is a time-dependent family $\{Φ_{t}\colon\mathbb{M}_{n}(\mathbb{C})\rightarrow\mathbb{M}_{n}(\mathbb{C})\}_{t\in\mat…
On Krull-Gabriel dimension of cluster repetitive categories and cluster-tilted algebras
Alicja Jaworska-Pastuszak, Grzegorz Pastuszak, Grzegorz Bobiński
Assume that is an algebraically closed field and denote by the Krull-Gabriel dimension of , where is a locally bounded -category (or a bound quiver -algebr…
Quantifier elimination theory and maps which preserve semipositivity
Grzegorz Pastuszak, Adam Skowyrski, Andrzej Jamiołkowski
We give an algorithm determining whether a hermiticity-preserving superoperator is positive. In our approach we apply techniques of quantifier elimination theory for real numbers.…