Representations of Smith algebras which are free over the Cartan subalgebra

• Type: Article in International Scientific Journal
• Date: 2024

Authors

Futorny, V (Author) Other; Samuel A Lopes (Author) FCUP; Mendonça, EM (Author) Other

Journal

Title: Journal of Algebra

Vol. 655

Pages: 405-423

ISSN: 0021-8693

Publisher: Elsevier

Indexing

ISI Web of Knowledge - 0 Citations

Scopus - 0 Citations

Other information

Authenticus ID: P-00Z-J00

DOI: 10.1016/j.jalgebra.2023.11.030

Abstract (EN): 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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 19