Deforming the Lie algebra of vector fields on $S^1$ inside the Lie algebra of pseudodifferential symbols on $S^1$

Roger, C.; Ovsienko, V.
Referencia bibliográfica

eprint arXiv:math/9812074

Fecha de publicación:
12
1998
Número de autores
2
Número de autores del IAC
0
Número de citas
1
Número de citas referidas
1
Descripción
We classify nontrivial deformations of the standard embedding of the Lie algebra $Vect(S^1)$ of smooth vector fields on the circle, into the Lie algebra~$PD(S^1)$ of pseudodifferential symbols on $S^1$. This approach leads to deformations of the central charge induced on $Vect(S^1)$ by the canonical central extension of $PD(S^1)$. As a result we obtain a quantized version of the second Bernoulli polynomial.