Abstract
Following Leites, we define a cohomology for Lie superalgebras. A number of combinatorial identities are presented as well as two theorems which prove to be very useful in calculations. We then introduce the notion of deformations of Lie superalgebras and look at the deformations of the super-Poincaré algebra and of osp(4/2).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
WhiteheadJ. H. C., Proc. Philos. Soc. 32, 229 (1936); Chevalley, C. and Eilenberg, S., Trans. Amer. Math. Soc. 63, 85 (1948).
HochschildG. and SerreJ. P., Ann. Math. 57, 591 (1953).
FlatoM., LichnerowiczA., and SternheimerD., J. Math. Phys. 17, 1754 (1976); Bayen, F., Flato, M., Fronsdal, C., Lichnerowicz, A., and Sternheimer, D., Ann. Phys. 111, 61 (1978).
PinczonG. and SimonJ., Rep. Math. Phys. 16, 49 (1979); Binegar, B., Fronsdal, C., and Heidenreich, W., Phys. Rev. D27, 2249 (1983).
BasartH., FlatoM., LichnerowiczA., and SternheimerD., Lett. Math. Phys. 8, 483 (1984).
KacsV. G., Funk. Anal. 9, 91 (1975).
LeitesD. A., Funk. Anal. 9, 75 (1975).
For a general discussion of deformation theory see, e.g., GerstenhaberM., Ann. Math. 79, 59 (1964); Nijenuis, A. and Richardson, R. W., Jr., Ann. Math. 72, 1 (1966).
ZuminoB., Nucl. Phys. B127, 189 (1977).
KacsV. G., Adv. Math. 26, 8 (1977).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Binegar, B. Cohomology and deformations of lie superalgebras. Letters in Mathematical Physics 12, 301–308 (1986). https://doi.org/10.1007/BF00402663
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00402663