Lie superbialgebra structures on the Lie superalgebra $({\mathcal{C}}^3+\mathcal{A})$ and deformation of related integrable Hamiltonian systems

Abstract

Admissible structure constants related to the dual Lie superalgebras of particular Lie superalgebra $({\mathcal{C}}^3+\mathcal{A})$ are found by straightforward calculations from the matrix form of super Jacobi and mixed super Jacobi identities which are obtained from adjoint representation. Then, by making use of the automorphism supergroup of the Lie superalgebra $({\mathcal{C}}^3+\mathcal{A})$, the Lie superbialgebra structures on the Lie superalgebra $({\mathcal{C}}^3+\mathcal{A})$ are obtained and classified into inequivalent 31 families. We also determine all corresponding coboundary and bi-r-matrix Lie superbialgebras. The quantum deformations associated with some Lie superbialgebras $({\mathcal{C}}^3+\mathcal{A})$ are obtained, together with the corresponding deformed Casimir elements. As an application of these quantum deformations, we construct a deformed integrable Hamiltonian system from the representation of the Hopf superalgebra ${U_{{}_{\lambda }}}^{({\mathcal{C}}_{p=1}^{2,\epsilon }\oplus {\mathcal{A}}_{1,1})}(({\mathcal{C}}^3+\mathcal{A}))$.

25 pages, 4 Tables

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• Integrable S-matrices, massive and massless modes and the AdS_2 x S^2 superstring
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Cited by in corpus (6)

• Yang-Baxter deformations of WZW model on the Heisenberg Lie group
• Yang-Baxter deformation of WZW model based on Lie supergroups: The cases of $GL(1|1)$ and $(C^3+A)$
• A hierarchy of WZW models related to super Poisson-Lie T-duality
• Cosmological string backgrounds from super Poisson-Lie T-plurality
• T-duality/plurality of BTZ black hole metric coupled to two fermionic fields
• More on (gauged) WZW models over low-dimensional Lie supergroups and their integrable deformations