The second cohomology spaces K(2) with coefficents in the superspace of weighted densities
DOI:
https://doi.org/10.37863/umzh.v72i10.6030Keywords:
Cohomologie, Lie superalgebra, weighted densitiesAbstract
UDC 515.1
Over the (1,2)-dimensional supercircle, we investigate the second cohomology space associated the lie superalgebra K(2) of vector fields on the supercircle S1|2 with coefficients in the space of weighted densities.
We explicitly give 2-cocycle spanning these cohomology spaces.
References
B. Agrebaoui, I. Basdouri, M. Boujelben, The second cohomology spaces of K(1) with coefficient in the superspace of weighted densities and deformation of the superspace of symbols on S1|1, Submetted, hal-01699198, v1.
I. Basdouri, On osp(1|2)-relative cohomology on S1|1, Commun. Algebra, 42, № 4, 1698 – 1710 (2014), DOI: 10.1080/00927872.2012.748782
I. Basdouri, M. Ben Ammar, Cohomology of osp(1|2) acting on linear differential operators on the supercercle S1|1, Lett. Math. Phys., 81, № 3, 239 – 251 (2007), DOI: 10.1007/s11005-007-0181-z
V. Ovsienko, C. Roger, Extension of Virasoro group and Virasoro algebra by modules of tensor densities on S1, Funct. Anal. and Appl., 30, № 4, 290 – 291 (1996), DOI: 10.1007/BF02509628
V. Ovsienko, P. Marcel, Extension of the Virasoro and Neveu – Schwartz algebras and generalized Sturm – Liouville operators, Lett. Math. Phys., 40, № 1, 31 – 39 (1997), DOI: 10.1007/s11005-007-0181-z
