Quasi-Hopf Superalgebras and Elliptic Quantum Supergroups
نویسندگان
چکیده
We introduce the quasi-Hopf superalgebras which are Z2 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 Bq,λ(G) and the vertex type Aq,p[ ̂ sl(n|n)] (and Aq,p[ ̂ 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 Uq[ ̂ sl(n|n)] in a non-standard system of simple roots, all of which are fermionic. Mathematics Subject Classifications (1991): 81R10, 17B37, 16W30
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