Abstract
UDC 515.12 We investigate the first cohomology space associated with the embedding of the Lie orthosymplectic superalgebra
o
s
p
(
n
|
2
)
on the
(
1
,
n
)
-dimensional superspace
ℝ
1
|
n
in the Lie superalgebra
𝒮
Ψ
D
O
(
n
)
(for
n
≥
4
) of superpseudodifferential operators with smooth coefficients. Following Ovsienko and Roger, we give explicit expressions of the basis cocycles.This work is the simplest generalization of a result by Basdouri [<em>First space cohomology of the orthosymplectic Lie superalgebra in the Lie superalgebra of superpseudodifferential operators</em>, Algebras and Representation Theory, <strong>16</strong>, 35-50 (2013)].
Publisher
Institute of Mathematics National Academy of Sciences of Ukraine
Subject
General Earth and Planetary Sciences,General Engineering,General Environmental Science
Reference18 articles.
1. B. Agrebaoui, N. Ben Fraj, On the cohomology of Lie superalgebra of contact vector fields on $S^{1/1}$, Bull. Soc. Roy. Sci. Liege, 73 (2004).
2. B. Agrebaoui, N. Ben Fraj, S. Omri, On the cohomology of Lie superalgebra of contact vector fields on $S^{1|2}$, J. Nonlinear Math. Phys., 13, № 4, 523 – 534 (2006), https://doi.org/10.2991/jnmp.2006.13.4.7
3. B. Agrebaoui, I. Basdouri, N. Elghomdi, S. Hammami, First space cohomology of the orthosymplectic Lie
4. superalgebra $frak{osp}(3|2)$ in the Lie superalgebra of superpseudodifferential operators, J. Pseudo-Different. Oper. and Appl., 7, 141 – 155 (2016), https://doi.org/10.1007/s11868-015-0140-x
5. I. Basdouri, First space cohomology of the orthosymplectic Lie superalgebra in the Lie superalgebra of superpseudodifferential operators, Algebras and Representation Theory, 16, 35 – 50 (2013); https://doi.org/10.1007/s10468-011-9292-4.