A universal formula for representing Lie algebra generators as formal power series with coefficients in the Weyl algebra

@inproceedings{Durov2006AUF,
  title={A universal formula for representing Lie algebra generators as formal power series with coefficients in the Weyl algebra},
  author={Nikolai Durov and Zoran {\vS}koda},
  year={2006}
}
  • Nikolai Durov, Zoran Škoda
  • Published 2006
Given a n-dimensional Lie algebra g over a field k ⊃ Q, together with its vector space basis X0 1 , . . . ,X 0 n, we give a formula, depending only on the structure constants, representing the infinitesimal generators, Xi = X 0 i t in g ⊗k k[[t]], where t is a formal variable, as a formal power series in t with coefficients in the Weyl algebra An. Actually, the theorem is proved for Lie algebras over arbitrary rings k ⊃ Q. We provide three different proofs, each of which is expected to be… CONTINUE READING
Highly Cited
This paper has 26 citations. REVIEW CITATIONS

From This Paper

Topics from this paper.

Citations

Publications citing this paper.
Showing 1-10 of 18 extracted citations

References

Publications referenced by this paper.
Showing 1-10 of 10 references

Stojić, New realizations of Lie algebra kappa-deformed Euclidean space

M. S. Meljanac
2006

Kontsevich, Deformation quantization of Poisson manifolds

M. Kontsevich
Lett. Math. Phys • 2003

Universal representations of Lie algebras by coderivations

E. Petracci
Bull. Sci. Math • 2003

A pseudo-analyzer approach to formal group laws not of operad type

R. Holtkamp
J. Algebra • 2001

Quantized moduli spaces of the bundles on the elliptic curve and their applications, Integrable structures of exactly solvable 2d models of QFT (Kiev

A. V. Odesskii, B. L. Feigin
NATO Sci. Ser. II Math. Phys. Chem., • 2000

Lie theory of formal groups over an operad

B. Fresse
J. Algebra • 1998

Nonlinear Poisson brackets, Moskva

M. Karasev, V. Maslov
Nauka 1991 (in Russian); Engl. transl.: AMS Transl. Math. Monog • 1993

Similar Papers

Loading similar papers…