Global Deformations of the Witt Algebra of Krichever-Novikov Type

Details Global Deformations of the Witt Algebra of Krichever-Novikov Type Global Deformations of the Witt Algebra of Krichever-Novikov Type

2002-06-11

arxiv.org/abs/math/0206114v2

Mathematics

Quantum Algebra

21 pages, only typing errors and references are updated, final version

Scientific paper

By considering non-trivial global deformations of the Witt (and the Virasoro) algebra given by geometric constructions it is shown that, despite their infinitesimal and formal rigidity, they are globally not rigid. This shows the need of a clear indication of the type of deformations considered. The families appearing are constructed as families of algebras of Krichever-Novikov type. They show up in a natural way in the global operator approach to the quantization of two-dimensional conformal field theory. In addition, a proof of the infinitesimal and formal rigidity of the Witt algebra is presented.

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