ZZ×ZZ-graded Lie algebras generated by the Virasoro algebra and sl2 1
نویسندگان
چکیده
The present paper is another step toward the classification of ZZ×ZZ-graded Lie algebras: we classify ZZ×ZZ-graded Lie algebras A = ⊕i,j∈ZZAi,j over a field IF of characteristic 0 with dimAi,j ≤ 1 for i, j ∈ ZZ, satisfying: (1) A0 = ⊕i∈ZZAi,0 ≃ Vir, the centerless Virasoro algebra, (2) A0,−1,A0,0,A0,1 span the 3-dimensional simple Lie algebra sl2, (3) A is generated by the centerless Virasoro algebra and sl2. These algebras include some rank 2 centerless Virasoro algebras, and some rank 2 Block algebras and their extensions. §
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