Existence of a multiplicative basis for a finitely spaced module over an aggregate

TL;DR

This paper proves a conjecture that finitely spaced modules over an aggregate possess a multiplicative basis, extending known results from finite-dimensional algebras to a broader class of modules.

Contribution

It establishes the existence of a multiplicative basis for finitely spaced modules over an aggregate, confirming a conjecture posed in earlier literature.

Findings

Proves the conjecture on multiplicative bases for finitely spaced modules.

Extends results from finite-dimensional algebras to modules over aggregates.

Provides a theoretical foundation for understanding module structures over aggregates.

Abstract

By [R. Bautista, P. Gabriel, A.V Roiter., L. Salmeron, Representation-finite algebras and multiplicative basis. Invent. Math. 81 (1985) 217-285.], a finite-dimensional algebra having finitely many isoclasses of indecomposable representations admits a multiplicative basis. In Sections 4.10-4.12 of [P. Gabriel, A. V. Roiter, Representations of finite-dimensional algebras. Encyclopaedia of Math. Sci., vol. 73, Algebra 8, Springer-Verlag, 1992] an analogous hypothesis was formulated for finitely spaced modules over an aggregate. We prove this conjecture.