Abstract 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] .

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关于 N = 2 超共形代数的非权重表示

摘要 在本文中，我们在未扭曲的 N = 2 超共形代数上构建了一个非权模块族。这些模块当被视为嘉当子代数（以中心为模）上的模块时没有等级 2。我们给出了这些模块的同构类的分类。此外，这些模块的所有子模块都是精确确定的。尤其是那些模块并不简单。对相应的简单商模块进行分类。此外，这些简单的模块当被限制为 N = 1 超共形代数的模块时，与 Yang 等人构建的模块一致。(2020) [27]。