On non-weight representations of the N = 2 superconformal algebras

In this paper, we construct a family of non-weight modules over the untwisted N=2 superconformal algebras. Those modules when regarded as modules over the Cartan subalgebra (modulo the center) are free of rank 2. We give a classification of isomorphism classes of such modules. Moreover, all submodul...

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Bibliographic Details
Published inJournal of pure and applied algebra Vol. 225; no. 3; p. 106529
Main Authors Yang, Hengyun, Yao, Yufeng, Xia, Limeng
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.03.2021
Subjects
[formula omitted] superconformal algebra
Cartan subalgebra
Non-weight module
17B66
Cartan subalgebra
Non-weight module
17B68
N=2 superconformal algebra
17B10
17B65
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Summary:In this paper, we construct a family of non-weight modules over the untwisted N=2 superconformal algebras. Those modules when regarded as modules over the Cartan subalgebra (modulo the center) are free of rank 2. We give a classification of isomorphism classes of such modules. Moreover, all submodules of such modules are precisely determined. In particular, those modules are not simple. The corresponding simple quotient modules are classified. Furthermore, these simple modules when restricted as modules over N=1 superconformal algebras coincide with those modules constructed in Yang et al. (2020) [27].
ISSN:0022-4049
1873-1376
DOI:10.1016/j.jpaa.2020.106529