Nonstandard Quantum Groups and Superisation

Details Nonstandard Quantum Groups and Superisation Nonstandard Quantum Groups and Superisation

1995-06-13

arxiv.org/abs/q-alg/9506015v1

Mathematics

Quantum Algebra

31 pages LATEX

Scientific paper

We obtain the universal R-matrix of the non-standard quantum group associated to the Alexander-Conway knot polynomial. We show further that this non-standard quantum group is related to the super-quantum group $U_qgl(1|1)$ by a general process of superization, which we describe. We also study a twisted variant of this non-standard quantum group and obtain, as a result, a twisted version of $U_qgl(1|1)$ as a $q$-supersymmetry of the exterior differential calculus of any quantum plane of Hecke type, acting by mixing the bosonic $x_i$ co-ordinates and the forms $d x_i$.

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