coordinatized by quantum tori

We use a fermionic extension of the bosonic module to obtain a class of B(0, N)-graded Lie superalgebras with nontrivial central extensions. 0 Introduction B(M − 1, N)-graded Lie superalgebras were first investigated and classified up to central extension by Benkart-Elduque (see also Garcia-Neher’s work in [GN]). Those root graded Lie superalgebras are a super-analog of root graded Lie algebras. Fermionic and bosonic representations for the affine Kac-Moody Lie algebras were studied by Frenkel [F1,2] and Kac-Peterson [KP]. Feingold-Frenkel [FF] constructed representations for all classical affine Lie algebras by using Clifford or Weyl algebras with infinitely many generators. They also obtained realizations for certain affine Lie superalgebras including the affine B(0, N). [G] gave bosonic and fermionic representations for the extended affine Lie algebra ̃ glN(Cq), where Cq is the quantum torus in two variables. [CG] constructed modules for some BCN -graded Lie algebras by considering a fermionic extension of the fermionic module. In this paper, we will consider a fermionic extension of the bosonic module to obtain a class of B(0, N)-graded Lie superalgebras with nontrivial central extensions. ∗Research was partially supported by NSERC of Canada and Chinese Academy of Science. This paper is dedicated to Professor Sheng Gong on the occasion of his 75th birthday.