The Loewy Structure of Certain Fixpoint Algebras, Part II

TL;DR

This paper investigates the Loewy structure of a class of finite-dimensional, split, symmetric, local algebras introduced earlier, revealing cases where their Loewy length reaches the upper bound and others where it does not.

Contribution

It extends the analysis of these algebras by determining their Loewy lengths and providing examples of strict inequalities, advancing understanding of their structural properties.

Findings

Loewy length often equals the established upper bound

Examples of strict inequality in Loewy length

Deeper insight into the structure of certain finite-dimensional algebras

Abstract

In Part I of this paper, we introduced a class of certain algebras of finite dimension over a field. All these algebras are split, symmetric and local. Here we continue to investigate their Loewy structure. We show that in many cases their Loewy length is equal to an upper bound established in Part I, but we also construct examples where we have a strict inequality.