Ramond and Neveu–Schwarz Algebras and Narrow Lie Superalgebras

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.