Quasi-Hopf Superalgebras and Elliptic Quantum Supergroups

Yao-Zhong Zhang; Mark D. Gould

doi:10.1063/1.533029

paper

Quasi-Hopf Superalgebras and Elliptic Quantum Supergroups

arXiv:math/9809156 · doi:10.1063/1.533029

Abstract

We introduce the quasi-Hopf superalgebras which are $Z_{2}$ graded versions of Drinfeld's quasi-Hopf algebras. We describe the realization of elliptic quantum supergroups as quasi-triangular quasi-Hopf superalgebras obtained from twisting the normal quantum supergroups by twistors which satisfy the graded shifted cocycle condition, thus generalizing the quasi-Hopf twisting procedure to the supersymmetric case. Two types of elliptic quantum supergroups are defined, that is the face type $B_{q, λ} (G)$ and the vertex type $A_{q, p} [s l (n ∣ n)^]$ (and $A_{q, p} [g l (n ∣ n)^]$ ), where $G$ is any Kac-Moody superalgebra with symmetrizable generalized Cartan matrix. It appears that the vertex type twistor can be constructed only for $U_{q} [s l (n ∣ n)^]$ in a non-standard system of simple roots, all of which are fermionic.

22 pages, Latex file

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Comments on Drinfeld Realization of Quantum Affine Superalgebra $U_{q} [g l (m ∣ n)^{(1)}]$ and its Hopf Algebra Structure

Quasi-Hopf Superalgebras and Elliptic Quantum Supergroups

Abstract

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