Infinitesimal semi-invariant pictures and co-amalgamation

TL;DR

This paper investigates the local structure of semi-invariant pictures of tame hereditary algebras near the null root, revealing a description via co-amalgamation and cluster-like structures, with invariance under cluster tilting.

Contribution

It introduces co-amalgamation to describe local semi-invariant structures and connects them to support regular clusters, advancing understanding of tame hereditary algebras.

Findings

Local structure described by semi-invariant pictures of self-injective Nakayama algebras

Support regular clusters characterize cones of the local structure

Local structure invariant under cluster tilting

Abstract

The purpose of this paper is to study the local structure of the semi-invariant picture of a tame hereditary algebra near the null root. Using a construction that we call co-amalgamation, we show that this local structure is completely described by the semi-invariant pictures of a collection of self-injective Nakayama algebras. We then describe the cones of this local structure using cluster-like structures that we call support regular clusters. Finally, we show that the local structure is (piecewise linearly) invariant under cluster tilting.