By taking the concept of weight conservation into account,new solations of Yang-Baxter equation without spectral parameter are obtained through the non-standard A-matrix on the feensorial space V^(1/2) (j≠1/2)in terms of the irreducible representation of the quantum universal enveloping algebra SLq(2).The non-standard R-matrix J?1/21 is obtained in an explicit form for j=1.
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