13 papers
Algebras of generalized quaternion type: biregular case
Karin Erdmann, Adam Hajduk, Adam Skowyrski
This paper provides the next step towards classification of algebras of generalized quaternion type. Previously algebras with 2-regular Gabriel quiver were classified (a quiver is…
Tame symmetric algebras of period four with small Gabriel quivers
Karin Erdmann, Alicja Jaworska-Pastuszak, Adam Skowyrski
The tame symmetric algebras of period four, TSP4 algebras for short, form an important class of algebras, with interesting links to various branches of modern algebra. The study of…
Iterated mutations of symmetric periodic algebras
Adam Skowyrski
Following methods used by A. Dugas for investigating derived equivalent pairs of (weakly) symmetric algebras, we apply them in a specific situation, obtaining new deep results conc…
A note on spherical algebras
Karin Erdmann, Adam Skowyrski
We classify tame symmetric algebras of period four which are closely related to the spherical algebras introduced in [7]. This note provides a classification in the special case wh…
Periodicity shadows II. Computational aspects
Jerzy Białkowski, Adam Skowyrski
This article provides the second part of the research initiated in arXiv:2411.17381, where we introduced and investigated so called periodicity shadows, which are special skew-symm…
Periodicity shadows I: A new approach to combinatorics of periodic algebras
Adam Skowyrski
This article is devoted to introduce a new notion of periodicity shadow, which appeared naturally in the study of combinatorics of tame symmetric algebras of period four, or more g…
Local structure of tame symmetric algebras of period four
Karin Erdmann, Adam Hajduk, Adam Skowyrski
In this paper we study the structure of Gabriel quivers of tame symmetric algebras of period four. More precisely, we focus on algebras having Gabriel quiver {\it biregular}, i.e.…
Tame symmetric algebras of period four
Karin Erdmann, Adam Hajduk, Adam Skowyrski
In this paper we are concerned with the structure of tame symmetric algebras of period four (TSP4 algebras, for short). We will mostly focus on the case when the Gabriel quiver of…
Generalized weighted surface algebras
Andrzej Skowroński, Adam Skowyrski
The weighted triangulation algebras associated to triangulation quivers and their socle deformations were recently introduced and studied in [15]-[20] and [2]. These algebras, base…
Virtual mutations of weighted surface algebras
Thorsten Holm, Andrzej Skowroński, Adam Skowyrski
The finite-dimensional symmetric algebras over an algebraically closed field, based on surface triangulations, motivated by the theory of cluster algebras, have been extensively in…
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.…
On maps which preserve semipositivity and quantifier elimination theory for real numbers
Grzegorz Pastuszak, Adam Skowyrski, Andrzej Jamiołkowski
Assume that is a superoperator which preserves hermiticity. We give an algorithm determining whether preserv…
Two tilts of higher spherical algebras
Adam Skowyrski
We introduce new symmetric and periodic algebras of period 4, which are tame of non-polynomial growth