A generalized super AKNS hierarchy associated with orthosymplectic Lie superalgebra OSP(2,2) and its super bi‐Hamiltonian structures

2020 ◽  
Vol 43 (6) ◽  
pp. 3076-3085
Author(s):  
Jing Yu ◽  
Jingwei Han ◽  
Chuanzhong Li
Keyword(s):  
Lie Superalgebra ◽  
Hamiltonian Structures ◽  
Akns Hierarchy ◽  
Orthosymplectic Lie Superalgebra

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].

HAMILTONIAN STRUCTURES OF TWO INTEGRABLE COUPLINGS OF THE MODIFIED AKNS HIERARCHY

2007 ◽  
Vol 21 (30) ◽  
pp. 2063-2074 ◽  
Author(s):  
YUFENG ZHANG ◽  
Y. C. HON
Keyword(s):  
Lie Algebra ◽  
Hamiltonian Structure ◽  
Three Dimensional ◽  
Hamiltonian Structures ◽  
Akns Hierarchy ◽  
Higher Dimensional ◽  
Integrable Couplings

The extension of a three-dimensional Lie algebra into two higher-dimensional ones is used to deduce two new integrable couplings of the m-AKNS hierarchy. The Hamiltonian structures of the two integrable couplings are obtained, respectively. Specially, the complex Hamiltonian structure of the second integrable couplings is given.

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].

THE AMITSUR–LEVITZKI THEOREM FOR THE ORTHOSYMPLECTIC LIE SUPERALGEBRA 𝔬𝔰𝔭(1, 2n)

2006 ◽  
Vol 05 (03) ◽  
pp. 307-332
Author(s):  
PIERRE-ALEXANDRE GIÉ ◽  
GEORGES PINCZON ◽  
ROSANE USHIROBIRA
Keyword(s):  
Lie Superalgebra ◽  
Lie Superalgebras ◽  
Orthosymplectic Lie Superalgebra ◽  
Cohomological Interpretation

Based on Kostant's cohomological interpretation of the Amitsur–Levitzki theorem, we prove a super version of this theorem for the Lie superalgebras 𝔬𝔰𝔭(1, 2n). We conjecture that no other classical Lie superalgebra can satisfy an Amitsur–Levitzki type super identity. We show several (super) identities for the standard super polynomials. Finally, a combinatorial conjecture on the standard skew supersymmetric polynomials is stated.

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