Abstract
By establishing a new boson realization of quantum universal enveloping algebra slq(2) and its representations in the non-generic case that q is a root of unity, the authors systematically construct non-generic R-matrices of slq(2) through the universal R-matrix. These new R-matrices are not covered by the standard R-matrices constructed in terms of quantum groups and the non-standard ones obtained by using the extended Kauffman's diagram technique.
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