scholarly journals Second cohomology space of the orthosymplectic Lie superalgebra with coefficients in the Lie superalgebra of superpseudodifferential operators

2016 ◽  
Vol 107 ◽  
pp. 99-113
Author(s):  
Othmen Ncib ◽  
Salem Omri
Keyword(s):  
Lie Superalgebra ◽  
Cohomology Space ◽  
Orthosymplectic Lie Superalgebra

𝔥-Relative cohomology on S1|1 and deformations

2018 ◽  
Vol 15 (12) ◽  
pp. 1850202
Author(s):  
Thamer Faidi
Keyword(s):  
Central Extension ◽  
Vector Fields ◽  
Central Charge ◽  
Lie Superalgebra ◽  
Relative Cohomology ◽  
Cohomology Space ◽  
Smooth Coefficients ◽  
Orthosymplectic Lie Superalgebra

Over the [Formula: see text]-dimensional supercircle [Formula: see text], we investigate the first [Formula: see text]-relative cohomology space associated with the embedding of the Lie superalgebra [Formula: see text] of contact vector fields in the Lie superalgebra [Formula: see text] of superpseudodifferential operators with smooth coefficients, where [Formula: see text] is the orthosymplectic Lie superalgebra. Likewise, we study the same problem for the affine Lie superalgebra [Formula: see text] instead of [Formula: see text]. We classify [Formula: see text]-trivial deformations of the standard embedding of the Lie superalgebra [Formula: see text] into the Lie superalgebra [Formula: see text]. This approach leads to the deformations of the central charge induced on [Formula: see text] by the canonical central extension of [Formula: see text].

The relative cohomology of the Lie superalgebra of contact vector fields on S1|2

2018 ◽  
Vol 15 (12) ◽  
pp. 1850203
Author(s):  
N. Ben Fraj ◽  
H. Khalfoun ◽  
T. Faidi
Keyword(s):  
Vector Fields ◽  
Lie Superalgebra ◽  
Module Structure ◽  
Relative Cohomology ◽  
Cohomology Space ◽  
Smooth Coefficients ◽  
Orthosymplectic Lie Superalgebra

Over the [Formula: see text]-dimensional supercircle [Formula: see text], we investigate the first [Formula: see text]-relative cohomology space associated with the embedding of the Lie superalgebra [Formula: see text] of contact vector fields in the Lie superalgebra [Formula: see text] of superpseudodifferential operators with smooth coefficients, where [Formula: see text] is the orthosymplectic Lie superalgebra. Likewise, we study the same problem for the affine Lie superalgebra [Formula: see text] instead of [Formula: see text]. We classify generic formal [Formula: see text]-trivial deformations of the [Formula: see text]-module structure on the superspace of the supercommutative algebra [Formula: see text] of pseudodifferential symbols on [Formula: see text].

Differential Representations of the Lie Superalgebra C(n+1)

2012 ◽  
Vol 19 (04) ◽  
pp. 745-754
Author(s):  
Yuezhu Wu ◽  
Xiaoqing Yue ◽  
Linsheng Zhu
Keyword(s):  
Coherent State ◽  
Finite Number ◽  
Differential Operators ◽  
Lie Superalgebra ◽  
Verma Modules ◽  
Singular Vectors ◽  
Orthosymplectic Lie Superalgebra

In this paper, we realize Verma modules and the vector-coherent-state (VCS) representations of the orthosymplectic Lie superalgebra osp(2|2n) as differential operators with vector coefficients. We also characterize simple sub-representations of VCS representations as kernels of some finite number of differential operators. The singular vectors of the atypical representation of osp(2|2n) are explicitly given.

Cohomology of orthosymplectic Lie superalgebra acting on λ-densities on ℝ1|n

2016 ◽  
Vol 14 (01) ◽  
pp. 1750016
Author(s):  
Nabila El Gomdi ◽  
Rim Messaoud
Keyword(s):  
Lie Superalgebra ◽  
Acta Math ◽  
Differential Cohomology ◽  
Orthosymplectic Superalgebra ◽  
Orthosymplectic Lie Superalgebra

We compute the first differential cohomology of the orthosymplectic Lie superalgebra [Formula: see text] with coefficients in the superspace of weighted densities [Formula: see text] on the (1, 2)-dimensional real superspace. We explicitly give 1-cocycles spanning these cohomologies. This work is the simplest generalization of a result by Basdouri and Essayari [On cohomology of the orthosymplectic superalgebra, Acta Math. Hungar. 130(1–2) (2011) 155–166].

On the 𝔞𝔣𝔣(m|1)-relative cohomology of the orthosymplectic superalgebra 𝔬𝔰𝔭(m|2) and 𝔞𝔣𝔣(m|1)-trivial deformation

2017 ◽  
Vol 14 (02) ◽  
pp. 1750027
Author(s):  
Hafedh Khalfoun ◽  
Thamer Faidi
Keyword(s):  
Lie Superalgebra ◽  
Lie Derivative ◽  
Relative Cohomology ◽  
Orthosymplectic Superalgebra ◽  
Orthosymplectic Lie Superalgebra ◽  
Cohomology Spaces

Over the [Formula: see text]-dimensional supercircle [Formula: see text], we consider the action of the orthosymplectic Lie superalgebra [Formula: see text], by the Lie derivative on the superpseudodifferential operators [Formula: see text]. We compute the [Formula: see text]-relative cohomology spaces [Formula: see text], where [Formula: see text] is the affine Lie superalgebra on [Formula: see text]. We explicitly give cocycles spanning these cohomology spaces. We study the [Formula: see text]-trivial deformations of the structure of the [Formula: see text]-modules [Formula: see text].

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