Z x Z-graded Lie algebras generated by the Virasoro algebra and $sl_2$

Details Z x Z-graded Lie algebras generated by the Virasoro algebra and $sl_2$ Z x Z-graded Lie algebras generated by the Virasoro algebra and $sl_2$

2003-04-03

arxiv.org/abs/math/0304035v1

Math. Nach. 246/247 (2002), 188-201

Mathematics

Quantum Algebra

13 pages, latex

Scientific paper

The present paper is another step toward the classification of $\Z\times\Z$-graded Lie algebras: we classify $\Z\times\Z$-graded Lie algebras $A=\oplus_{i,j\in\Z}A_{i,j}$ over a field $F$ of characteristic 0 with dim $A_{i,j}\le1$ for $i,j\in\Z$, satisfying: (1) $\AA_0=\oplus_{i\in \Z}\AA_{i,0}$ is isomorphic to the centerless Virasoro algebra, (2) $A_{0,-1},A_{0,0},A_{0,1}$ span the 3-dimensional simple Lie algebra $sl_2$, (3) $A$ is generated by the centerless Virasoro algebra and $sl_2$. These algebras include some rank 2 centerless Virasoro algebras, and some rank 2 Block algebras and their extensions.

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