Lie Super-bialgebra Structures Research Articles

Lie super-bialgebra structures on the two dimensional supersymmetric Galilean conformal algebra

Let be the two dimensional supersymmetric Galilean conformal algebra. In this paper, we obtain that Lie superalgebra admits only triangular coboundary Lie super-bialgebra structures and the proof is mainly based on the computation of the first cohomology group of with coefficients in the tensor product of its adjoint module.

Quantization of the Lie superalgebra of Witt type

In this paper, we use the quantization technique by a Drinfel’d twist to quantize the Lie superalgebra of Witt type, whose Lie super-bialgebra structures were recently determined by Yue and Zhu, and we obtain a new class of non-commutative and non-cocommutative Hopf superalgebras.

Lie super-bialgebra structures on the N = 2 super-BMS3 algebra

In this paper, Lie super-bialgebra structures on the [Formula: see text] super-BMS3 algebra are investigated. By computing derivations from the super-BMS3 to the tensor product of its adjoint module, we obtain that all Lie bialgebra structures on the [Formula: see text] super-BMS3 Algebra are triangular coboundary.

Lie super-bialgebra structures on the Lie superalgebra of Witt type

In this article, Lie super-bialgebra structures on the Lie superalgebra of Witt type are investigated. They are shown to be triangular coboundary. As a byproduct, we obtain that the first cohomology group is trivial.

Lie Super-bialgebra Structures on the Super-BMS3 Algebra

In this paper, Lie super-bialgebra structures on the super-BMS3 algebra are considered. It is proved that all such Lie super-bialgebras are triangular coboundary Lie super-bialgebras. The method we use is mainly based on the computation of derivations from the super-BMS3 to the tensor product of its adjoint module.

Lie super-bialgebra structures on a class of generalized super W-algebra

In this paper, Lie super-bialgebra structures on a class of generalized super W-algebra are investigated. By proving the first cohomology group of with coefficients in its adjoint tensor module is trivial, namely, , we obtain that all Lie super-bialgebra structures on are triangular coboundary.

Lie superbialgebra structures on the Lie superalgebra C3+A and deformation of related integrable Hamiltonian systems

Admissible structure constants related to the dual Lie superalgebras of particular Lie superalgebra (C3+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 (C3+A), the Lie superbialgebra structures on the Lie superalgebra (C3+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 (C3+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 Uλ(Cp=12,𝜖⊕A1,1)(C3+A).

Lie super-bialgebra structures on super W-algebra SW(32,32)

Super W -algebra SW ( 3 2 , 3 2 ) is the supersymmetric extension of Galilean conformal algebra in 2d. In this paper, we obtain that super W -algebra SW ( 3 2 , 3 2 ) admits only triangular coboundary Lie super-bialgebra structures and the proof is mainly based on the computation of the first cohomology group of SW ( 3 2 , 3 2 ) with coefficients in the tensor product of its adjoint module.

LIE SUPER-BIALGEBRAS ON GENERALIZED LOOP SUPER-VIRASORO ALGEBRAS

In this article we consider Lie super-bialgebra structures on the generalized loop super-Virasoro algebra <TEX>${\mathcal{G}}$</TEX>. By proving that the first cohomology group <TEX>$H^1({\mathcal{G}},{\mathcal{G}}{\otimes}{\mathcal{G}})$</TEX> is trivial, we obtain that all such Lie bialgebras are triangular coboundary.

Lie super-bialgebra and quantization of the super Virasoro algebra

In this paper, we study Lie super-bialgebra and quantization of the super Virasoro algebra, whose even part is the centerless twisted Heisenberg-Virasoro algebra. By using some Liu-Pei-Zhu’s results, we prove that all Lie super-bialgebra structures on the super Virasoro algebra are triangular coboundary. Furthermore, we quantize the super Virasoro algebra by the Drinfel’d twist quantization technique and obtain a class of noncommutative and noncocommutative Hopf superalgebras.

Lie Super-bialgebra Structures on Generalized Ramond N=2 Super-Virasoro Algebras

In this paper, Lie super-bialgebra structures on generalized Ramond N=2 super-Virasoro algebras [Formula: see text] are determined. It is proved that all Lie super-bialgebras are coboundary triangular Lie super-bialgebras.

Lie superbialgebra structures on the [formula omitted] superconformal Neveu–Schwarz algebra

In this paper, Lie superbialgebra structures on the N=2 superconformal Neveu–Schwarz algebra are considered by a very simple method. We prove that every Lie superbialgebra structure on the algebra is triangular coboundary.

Lie Super-bialgebra Structures on the Centerless Twisted N=2 Super-conformal Algebra

In this paper, Lie super-bialgebra structures on the centerless twisted N=2 super-conformal algebra [Formula: see text] are considered, which are proved to be coboundary triangular.

Lie super-bialgebra structures on generalized super-Virasoro algebras

In this article, Lie super-bialgebra structures on generalized super-Virasoro algebras ℒ are considered. It is proved that all such Lie super-bialgebras are coboundary triangular Lie super-bialgebras if and only if H 1(ℒ, ℒ ⊗ ℒ)=0.

Lie super-bialgebra structures on super-Virasoro algebra

In this paper we obtain that every super-Virasoro algebra admits only triangular coboundary Lie super-bialgebra structures and this is proved mainly based on the computation of derivations from the super-Virasoro algebra to the tensor product of its adjoint module.

Lie super-bialgebra structures on the Ramond N = 2 super-virasoro algebra

In this paper, Lie super-bialgebra structures on Ramond N = 2 super-Virasoro algebras L are considered. It is proved that all such Lie super-bialgebras are coboundary triangular Lie super-bialgebras.

Classification of low-dimensional Lie super-bialgebras

A thorough analysis of Lie super-bialgebra structures on Lie super-algebras osp(1;2) and super e(2) is presented. A combined technique of computer algebraic computations and subsequent identification of equivalent structures is applied. In all the cases, Poisson–Lie brackets on supergroups are found. The possibility of quantizing them in order to obtain quantum groups is discussed. It turns out to be straightforward for all but one structure for the super-E(2) group.