BALINSKY–NOVIKOV SUPERALGEBRAS AND SOME INFINITE-DIMENSIONAL LIE SUPERALGEBRAS

In this paper, we recall the Balinsky–Novikov (BN) superalgebras and revisit the approach of constructing an infinite-dimensional Lie superalgebra by a kind of affinization of a BN superalgebra. As an example, we give an explicit construction of Beltrami and Green–Schwarz–Witten (GSW) algebras from two isomorphic BN superalgebras, respectively, which proves that they are isomorphic as a direct consequence. Moreover, we consider the central extensions of the infinite-dimensional Lie superalgebras induced from BN superalgebras through certain bilinear forms on their corresponding BN superalgebras.