Z x Z-graded Lie algebras generated by the Virasoro algebra and sl₂

2003/04/03 by Yucai Su, Jiengfeng Zhang, Kaiming Zhao
Mathematics · #math.QA #msc:17B36

paper · pdf

published as Math. Nach. 246/247 (2002), 188-201 · 13 pages, latex

arxiv created 2003/04/03 · arxiv updated 2009/11/30

Abstract

The present paper is another step toward the classification of \Z×\Z-graded Lie algebras: we classify \Z×\Z-graded Lie algebras A=⊕_i,j∈\ZA_i,j over a field F of characteristic 0 with dim A_i,j≤1 for i,j∈\Z, satisfying: (1) Å₀=⊕_{i∈ \Z}Å_i,0 is isomorphic to the centerless Virasoro algebra, (2) A_0,-1,A_0,0,A_0,1 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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