Scholarlink

<p>The loop Neveu–Schwarz algebra is the Lie superalgebra of the tensor product of the <i>N</i> = 1 Neveu–Schwarz algebra and the Laurent polynomial algebra. This paper classifies simple Harish-Chandra modules over the loop Neveu–Schwarz algebra, which turn out to be highest weight modules, lowest weight modules and evaluation modules of the intermediate series (all weight spaces are one-dimensional). As a by-product, we obtain a classification of simple Harish-Chandra modules over the truncated Neveu–Schwarz algebra. We also determine the necessary and sufficient conditions for highest weight simple modules over the loop Neveu–Schwarz algebra to have all finite-dimensional weight spaces, as well as the necessary and sufficient conditions for highest weight Verma modules to be simple.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Classification of the simple Harish-Chandra modules over the loop Neveu–Schwarz algebra

  • 期刊论文

  • 发表日期：

    2025年9月29日

查看全文
  • Qingyan Wu,
  • Dong Liu,
  • Yufeng Pei

摘要

The loop Neveu–Schwarz algebra is the Lie superalgebra of the tensor product of the N = 1 Neveu–Schwarz algebra and the Laurent polynomial algebra. This paper classifies simple Harish-Chandra modules over the loop Neveu–Schwarz algebra, which turn out to be highest weight modules, lowest weight modules and evaluation modules of the intermediate series (all weight spaces are one-dimensional). As a by-product, we obtain a classification of simple Harish-Chandra modules over the truncated Neveu–Schwarz algebra. We also determine the necessary and sufficient conditions for highest weight simple modules over the loop Neveu–Schwarz algebra to have all finite-dimensional weight spaces, as well as the necessary and sufficient conditions for highest weight Verma modules to be simple.