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arXiv · 2308.07881

Representations of Smith algebras which are free over the Cartan subalgebra

Vyacheslav Futorny·Samuel A. Lopes·Eduardo M. Mendonça
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Abstract

In this paper, we study the category of modules over the Smith algebra which are free of finite rank over the unital polynomial subalgebra generated by the Cartan element $h$ and obtain families of such simple modules of arbitrary rank. In the case of rank one we obtain a full description of the isomorphism classes, a simplicity criterion, and an algorithm to produce all composition series. We show that all such modules have finite length and describe the composition factors and their multiplicity.

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BibTeXRIS

Vyacheslav Futorny, Samuel A. Lopes, Eduardo M. Mendonça. 2023-08-15. Representations of Smith algebras which are free over the Cartan subalgebra. https://doi.org/10.1016/j.jalgebra.2023.11.030

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