Representations of Smith algebras which are free over the Cartan subalgebra
| Autor: | Futorny, Vyacheslav, Lopes, Samuel A., Mendonça, Eduardo M. |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.jalgebra.2023.11.030 |
| Popis: | 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. Comment: 16 pages |
| Databáze: | arXiv |
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