In this paper, we get the general solutions of 4×4 singular upper triangle quantum coloured Yang-Baxter matrix equation. This paper has three chapters. In the first chapter, the artical introduce some symbols and tell us which we want to solve, then give the principal results. In the second chapter, we give some lemmas which will be used in the next chapter. In the third chaper, we give the general solutions of 4×4 singular upper triangle quantum coloured Yang-Baxter matrix equation in half of all cases.
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