Periodicity shadows II. Computational aspects

TL;DR

This paper explores computational methods for identifying tame periodicity shadows, extending previous theoretical work by providing algorithms and enumerations for small sizes in the context of symmetric algebras.

Contribution

It introduces an algorithm to compute all tame periodicity shadows of a given size and enumerates these shadows for sizes up to 6.

Findings

Developed an algorithm for computing tame periodicity shadows.

Enumerated all tame periodicity shadows of sizes up to 6.

Extended theoretical results with computational data.

Abstract

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-symmetric matrices related to symmetric algebras with periodic simple modules. In arXiv:2411.17381 we focused on theoretical aspects, whereas here we present complementary cosiderations concerning computational issues. Namely, we discuss an algorithm, which computes all tame periodicity shadows of given size (see Section 2), and then present lists of all tame periodicity shadows of small sizes, that is at most 6.