Abstract

Two one-parameter families of positively graded Lie superalgebras generated by two elements and two relations that are narrow in the sense of Zelmanov and Shalev are considered. The first family contains the positive part R⁺ of the Ramond algebra, while the second one contains the positive part NS⁺ of the Neveu–Schwarz algebra. The results of the article are super analogues of Benoist’s theorem on defining the positive part of the Witt algebra by generators and relations.

中文翻译：

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Ramond 和 Neveu-Schwarz 代数与窄李超代数

摘要

考虑由两个元素和两个 Zelmanov 和 Shalev 意义上的狭义关系生成的两个单参数族正分级李超代数。第一个族包含 Ramond 代数的正部分R ⁺ ，而第二个族包含Neveu-Schwarz 代数的正部分NS ^{+ 。}这篇文章的结果是贝诺伊斯特通过生成元和关系定义维特代数的正部分的定理的超级类似物。