The dimensions of the homomorphism spaces to indecomposable modules over the four subspace algebra

TL;DR

This paper provides detailed formulas and descriptions for the dimensions of homomorphism spaces to indecomposable modules over the four subspace algebra, completing previous work with full proofs and classifications.

Contribution

It offers the complete proof of key formulas and a full classification of indecomposable modules for the four subspace algebra, advancing understanding of its module category.

Findings

Explicit formulas for homomorphism space dimensions

Full classification of indecomposable modules

Complete proof of key propositions

Abstract

This is the addendum to the paper "On the Multiplicity Problem and the Isomorphism Problem for the Four Subspace Algebra" Communications in Algebra, 40:6 (2012), 2005-2036 (DOI: 10.1080/00927872.2011.570830). We give here the full proof of Proposition 3.3, describing the formulas for the dimensions of the homomorphism spaces to indecomposable modules over the four subspace algebra \Lambda. The reader can also find here the full description of indecomposable \Lambda-modules.