On the Cohomology of the Lie Superalgebra of Contact Vector Fields onS^1|m

Cohomology of Lie superalgebras

“…In the case of Lie algebras we can mention, for instance, [4][5][6][7][8][9][10][11]. For Lie superalgebras there are several results regarding low dimensional degree cohomology for particular Lie superalgebras (see for instance [12][13][14][15]), and very few containing the hole picture (see for instance [16][17][18][19][20][21]).…”

The First Cohomology of the Superconformal Algebra K(1|4)

“…K(1|2N + 1) has a similar realization, and it will be discussed in detail in another paper. Note that the realization, which we consider here is different from the realization of K(1|N ) in [2][3][4][5][6], where the authors consider the natural embedding of K(1|N ) into the Lie superalgebra of symbols of pseudodifferential operators on S 1|N , which contracts to the Poisson superalgebra P (2|2N ).…”

“…Certain superizations of the constructions considered in [14,15] were obtained in [2][3][4][5][6]. In [2,3,5], the authors described the infinitesimal deformations of the natural embedding of the Lie superalgebra K(1|N ) of contact vector fields on the supercircle S 1|N into the Lie superalgebra of symbols of pseudodifferential operators on S 1|N for N = 1, 2 and 3, respectively.…”

“…In [2,3,5], the authors described the infinitesimal deformations of the natural embedding of the Lie superalgebra K(1|N ) of contact vector fields on the supercircle S 1|N into the Lie superalgebra of symbols of pseudodifferential operators on S 1|N for N = 1, 2 and 3, respectively. In [5] the authors also discussed the difficulties in generalizing their result from S 1|3 to the case S 1|N with N ≥ 4. In [6] and [4] the authors computed the obstructions to integrability and classified nontrivial deformations of these embeddings for N = 1 and 2, respectively.…”