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

Bibcode
1998math.....12074R
Roger, C.; Ovsienko, V.
Bibliographical reference

eprint arXiv:math/9812074

Advertised on:
12
1998
Number of authors
2
IAC number of authors
0
Citations
1
Refereed citations
1
Description
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.
Type
Non-refereed

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