arXiv subjects

C. Roger

Publications and source records attributed to C. Roger.

4 recordsLinked to original sources

arXiv1998

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

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.

math.QA↗

arXiv1997

Deforming the Lie algebra of vector fields on $S^1$ inside the Poisson algebra on $\dot T^*S^1$

We study deformations of the standard embedding of the Lie algebra $\Vect(S^1)$ of smooth vector fields on the circle, into the Lie algebra of functions on the cotangent bundle $T^*S^1$ (with respect to the Poisson bracket). We consider two analogous but different problems: (a) formal deformations of the standard embedding of $\Vect(S^1)$ into the Lie algebra of functions on $\dot T^*S^1:=T^*S^1\setminusS^1$ which are Laurent polynomials on fibers, and (b) polynomial deformations of the $\Vect(S^1)$ subalgebra inside the Lie algebra of formal Laurent series on $\dot T^*S^1$.

q-alg↗

arXiv1996

Extension of the Virasoro and Neveu-Schwartz algebras and generalized Sturm-Liouville operators

We consider the universal central extension of the Lie algebra $\Vect (S^1)${\math \s}$ C^{\infty}(S^1)$. The coadjoint representation of this Lie algebra has a natural geometric interpretation by matrix analogues of the Sturm-Liouville operators. This approach leads to new Lie superalgebras generalizing the well-known Neveu-Schwartz algebra.

hep-th↗

arXiv1994

Extensions of Virasoro group and Virasoro algebra by modules of tensor-densities on $S^1$

We classify non-trivial (non-central) extensions of the group $Diff^+(S^1)$ of all diffeomorphisms of the circle preserving its orientation and of the Lie algebra $Vect (S^1)$ of vector fields on $S^1$, by the modules of tensor-densities on $S^1$. The result is: 4 non-trivial extensions of $Diff^+(S^1)$ and 7 non-trivial extensions of $Vect (S^1)$. Analogous results hold for the Virasoro group and the Virasoro algebra. We also classify central extensions of constructed Lie algebras. CPT-94/P.3024

hep-th↗