Abstract
We prove the existence of a * product on the cotangent bundle of a parallelizable manifold M. When M is a Lie group the properties of this * product allow us to define a linear representation of the Lie algebra of this group on L 2(G), which is, in fact, the one corresponding to the usual regular representation of G.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Bayen, F., Flato, M., Fronsdal, C., Lichnerowicz, A., and Sternheimer, D., Ann. Phys. 111, 61–151 (1978).
Lichnerowicz, A., Lett. Math. Phys. 2, 133–143 (1977).
Moyal, J., Proc. Cambridge Phil. Soc. 45, 99–124 (1949).
Neroslavski, O.M. and Vlassov, A., C.R. Acad. Sci. Paris I, 292, 71 (1981).
Vey, J., Comm. Math. Helv. 50, 421–454 (1975).
Author information
Authors and Affiliations
Additional information
Chargé de recherches au FNRS.
Rights and permissions
About this article
Cite this article
Cahen, M., Gutt, S. Regular * representations of lie algebras. Letters in Mathematical Physics 6, 395–404 (1982). https://doi.org/10.1007/BF00419321
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00419321