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On Indecomposable Ideals Over Some Algebras

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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.

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Authors and Affiliations

  1. Department of Mathematics “G. Peano”, University of Turin, Via Carlo Alberto 10, I-10123, Torino, Italy

    Alessandro Ardizzoni

  2. Department of Mathematics and Computer Science, University of Ferrara, Via Machiavelli 30, Ferrara, I-44121, Italy

    Fabio Stumbo

Authors
  1. Alessandro Ardizzoni
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  2. Fabio Stumbo
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Corresponding author

Correspondence to Alessandro Ardizzoni.

Additional information

Presented by: Michela Varagnolo

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This note was written while the first author was member of the “National Group for Algebraic and Geometric Structures, and their Applications” (GNSAGA-INdAM). We would like to thank Michela Ceria for meaningful discussions on the topics treated in the present paper. We are also in debt with Lea Terracini for her contribution in the computations of the indecomposable ideals of the Taft algebra and their orthogonals. Finally we are grateful to the referee for useful comments.

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Ardizzoni, A., Stumbo, F. On Indecomposable Ideals Over Some Algebras. Algebr Represent Theor 23, 1443–1466 (2020). https://doi.org/10.1007/s10468-019-09900-9

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  • DOI: https://doi.org/10.1007/s10468-019-09900-9

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