On Indecomposable Ideals Over Some Algebras

TL;DR

This paper studies the structure of indecomposable ideals in certain algebras with bilinear forms, focusing on their classification and duality properties in specific algebraic contexts.

Contribution

It introduces new methods to classify right ideals and analyze their duals in algebras like cyclic group algebras, Taft algebras, and bosonization-based Hopf algebras.

Findings

Classification of right ideals in studied algebras

Characterization of dual ideals using bilinear forms

Insights into the structure of indecomposable ideals

Abstract

In this paper we investigate a family of algebras endowed with a suitable non-degenerate bilinear form that can be used to define two different notions of dual for a given right ideal. We apply our results to the classification of the right ideals and their duals in the cyclic group algebra, in the Taft algebra and in another example of Hopf algebra arising as bosonization.