An elementary proof of the vanishing of the second cohomology of the Witt and Virasoro algebra with values in the adjoint module

Details An elementary proof of the vanishing of the second cohomology of the Witt and Virasoro algebra with values in the adjoint module An elementary proof of the vanishing of the second cohomology of the Witt and Virasoro algebra with values in the adjoint module

2011-11-28

arxiv.org/abs/1111.6625v3

Mathematics

Rings and Algebras

prepared for publications, typos corrected, mentioned that the result is true for every field of char 0

Scientific paper

By elementary and direct calculations the vanishing of the (algebraic) second Lie algebra cohomology of the Witt and the Virasoro algebra with values in the adjoint module is shown. This yields infinitesimal and formal rigidity or these algebras. The first (and up to now only) proof of this important result was given 1989 by Fialowski in an unpublished note. It is based on cumbersome calculations. Compared to the original proof the presented one is quite elegant and considerably simpler.

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