a Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia
b Bauman Moscow State Technical University, Moscow, Russia
Correspondence to: *e-mail: dmitry.millionschikov@math.msu.ru
Correspondence to: **e-mail: fedya–57@yandex.ru
Received 11 November, 2023
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.
Keywords: Lie superalgebra, positive grading, narrow algebras, central extension, Ramond algebra, Neveu–Schwarz algebra
DOI: 10.1134/S1064562424701710