Non-trivial central extensions of Lie algebras of differential operators in two and higher dimensions

@article{Radul1991NontrivialCE,
  title={Non-trivial central extensions of Lie algebras of differential operators in two and higher dimensions},
  author={Andrey Radul},
  journal={Physics Letters B},
  year={1991},
  volume={265},
  pages={86-91}
}
  • A. Radul
  • Published 8 August 1991
  • Mathematics
  • Physics Letters B
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24 Citations
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References

SHOWING 1-10 OF 13 REFERENCES
On a trace functional for formal pseudo-differential operators and the symplectic structure of the Korteweg-devries type equations
We study the Lie geometric structure behind the Hamiltonian structure of the Korteweg deVries type equations.
Lie algebras and equations of Korteweg-de Vries type
The survey contains a description of the connection between the infinite-dimensional Lie algebras of Kats-Moody and systems of differential equations generalizing the Korteweg-de Vries and…
Hamiltonian reduction and conformal symmetries in two dimensions
Path integral quantization of the coadjoint orbits of the virasoro group and 2-d gravity
Infinite family of polynomial functions of the Virasoro generators with vanishing Poisson brackets
Infinite Conformal Symmetry in Two-Dimensional Quantum Field Theory - Nucl. Phys. B241, 333 (1984)
Cubic interaction in extended theories of massless higher-spin fields
Quantum Geometry of Bosonic Strings
HeiddenSL(n) symmetry in conformal field theories
We prove that an irreducible representation of the Virasoro algebra can be extracted from an irreducible representation space of theSL(2, ℛ) current algebra by putting a constraint on the latter…
Linearized curvatures for auxiliary fields in the de Sitter space
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