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Nonstandard quantum groups and superization
Author(s) -
Shahn Majid,
M. J. Rodríguez-Plaza
Publication year - 1995
Publication title -
journal of mathematical physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.708
H-Index - 119
eISSN - 1089-7658
pISSN - 0022-2488
DOI - 10.1063/1.531344
Subject(s) - quantum group , quantum , mathematics , pure mathematics , group (periodic table) , supersymmetry , differential calculus , mathematical physics , physics , quantum mechanics , algebra over a field
We obtain the universal R-matrix of the non-standard quantum group associatedto the Alexander-Conway knot polynomial. We show further that this non-standardquantum group is related to the super-quantum group $U_qgl(1|1)$ by a generalprocess of superization, which we describe. We also study a twisted variant ofthis 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 ofany quantum plane of Hecke type, acting by mixing the bosonic $x_i$co-ordinates and the forms $d x_i$.

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