Ramond, Neveu–Schwarz algebras and narrow Lie superalgebras

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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 Ramon algebra, 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.

About the authors

D. V. Millionshchikov

Steklov Mathematical Institute of Russian Academy of Sciences

Author for correspondence.
Email: dmitry.millionschikov@math.msu.ru
Russian Federation, Moscow

Th. I. Pokrovsky

Bauman Moscow State Technical University

Email: fedya-57@yandex.ru
Russian Federation, Moscow

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