Infinitesimal semi-invariant pictures and co-amalgamation

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.

v3: accepted manuscript. v2: improved and expanded exposition, notation, and references; replaced definition of co-amalgamation with a more general version (Definition 2.1.7). 48 pages, 6 figures