Combinatorics of faithfully balanced modules

William Crawley-Boevey, Biao Ma, Baptiste Rognerud, Julia Sauter

Published 2019-05-02Version 1

We study and classify faithfully balanced modules for the algebra of lower triangular $n$ by $n$ matrices. The theory extends known results about tilting modules, which are classified by binary trees, and counted with the Catalan numbers. The number of faithfully balanced modules is a $2$-factorial number. Among them are $n!$ modules with $n$ indecomposable summands, which can be classified by interleaved binary trees or by increasing binary trees.