Abstract
Starting from work of F. A. Berezin, in this Letter we define an invariant *-product on every nonexceptional Kähler symmetric space. We then obtain a recursion formula to calculate the corresponding invariant Hochschild 2-cochains for types I and IV spaces.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
BayenF., FlatoM., FronsdalC., LichnerowiczA. and SternheimerD.,Ann. Phys. 111, 61–151 (1978).
LichnerowiczA.,Ann. Di Math. 123, 287–330 (1980).
BerezinF. A.,Math. USSR. Izvestija 9, 341 (1975).
BerezinF. A.,Math. USSR. Izvestija 8, 1109 (1974).
Moreno, C., ‘Produits * et représentations des groupes de Lie compacts semisimples’, Séminaire Lichnerowicz au Collège de France le 14 janvier 1984.
Gutt, S. and Cahen, M., ‘An algebraic construction of *-products on the regular orbits of semi-simple Lie Groups’, preprint, to appear in the book in honor of Ibor Robinson.
LichnerowiczA.,Lett. Math. Phys. 2, 133–143 (1977).
LichnerowiczA.,Géométrie des groupes de transformations, Dunod, Paris, 1958.
CalabiE.,Ann. Math. 58, 1–23 (1953).
Lichnerowicz, A., ‘Espaces homogènes Khäleriens’, Actes du Coll. Int. de Géométrie Différentielle, Strasbourg (1953), 171–184.
Hua, L. K.,Harmonic Analysis of Functions of Several Complex Variables in the Classical Domains, Amer. Math. Soc., 1963.
MoritaK.,Sci. Rep. Tokyo Kyoiku Daigaku, Sec. A 5, 190–212 (1956).
BasartH. and LichnerowiczA.,C.R. Acad. Sci. Paris 295, 685 (1982).
Lichnerowicz, A., Cours au Collège de France, 1985–86.
De Wilde, M. and Lecompte, P., ‘Existence of Star Products and of Formal Deformations of the Poisson Algebra of Arbitrary Symplectic Manifolds’, Preprint.
GuttS.,Ann. Inst. Henri Poincaré 33, 1–31 (1981).
HamouiA. and LichnerowiczA.,J. Math. Phys. 25, 923–931 (1984).
BasartH., FlatoM., LichnerowiczA., and SternheimerD.,Lett. Math. Phys. 8, 483–494 (1984).
DeWildeM. et al.,J. Geom. Phys. 2, 121–129 (1985).
MorenoC. and Ortega-NavarroP.,Ann. Inst. Henri Poincaré,38, 215–241 (1983).
ArnalD.,Pac. J. Math. 114, 285–308 (1984).
Cahen, M. and Gutt, S., ‘Regular * Representations of Compact Lie Groups’, Preprint.
LichnerowiczA.,Ann. Inst. Fourier 32, 157–209 (1982).
CombetE.,Intégrales exponentielles, Lecture Notes in Math. No. 937, Springer-Verlag, Berlin, 1982.
FedoryukM. V.,Mat. Sb. 71, 65–115 (1970).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Moreno, C. *-Products on some Kähler manifolds. Lett Math Phys 11, 361–372 (1986). https://doi.org/10.1007/BF00574162
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00574162