Quasi-Hopf Superalgebras and Elliptic Quantum Supergroups
Zhang, Yao-Zhong ; Gould, Mark D.
arXiv, 9809156 / Harvested from arXiv
Text on arXiv
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 $B_{q,\lambda}(G)$ and the vertex type $A_{q,p}[\hat{sl(n|n)}]$ (and $A_{q,p}[\hat{gl(n|n)}]$), where $G$ is any Kac-Moody superalgebra with symmetrizable generalized Cartan matrix. It appears that the vertex type twistor can be constructed only for $U_q[\hat{sl(n|n)}]$ in a non-standard system of simple roots, all of which are fermionic.
Publié le : 1998-09-28
Classification:  Mathematics - Quantum Algebra,  High Energy Physics - Theory,  Mathematical Physics,  Nonlinear Sciences - Exactly Solvable and Integrable Systems 
@article{9809156,
     author = {Zhang, Yao-Zhong and Gould, Mark D.},
     title = {Quasi-Hopf Superalgebras and Elliptic Quantum Supergroups},
     journal = {arXiv},
     volume = {1998},
     number = {0},
     year = {1998},
     language = {en},
     url = {http://dml.mathdoc.fr/item/9809156}
}

Zhang, Yao-Zhong; Gould, Mark D. Quasi-Hopf Superalgebras and Elliptic Quantum Supergroups. arXiv, Tome 1998 (1998) no. 0, . http://gdmltest.u-ga.fr/item/9809156/