Abstract
The Virasoro algebra, defined by the basis elements {Ln,cˆ}n∈Z with commutation relations [Lm,Ln]=(m−n)Lm+n+δm+n,0⋅(Cmcˆ) and [Lm,cˆ]=0, is an infinite-dimensional Lie algebra with many applications in various areas of Mathematics and Theoretical Physics. Here the symbol δi,j denotes the Kronecker delta and Cm=(m(m2−1))/12. This algebra admits a natural Z-grading. Over an infinite field of characteristic different from 2 and 3, we describe the graded identities of the Virasoro algebra for this grading. It turns out that all these Z-graded identities are consequences of a collection of polynomials of degree 2, 3 and 4 and that they do not admit a finite basis.
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