Abstract
We consider SU q (2) covariant\(\hat R\)-matrices for the reducible3 ⊕1 representation. There are three solutions to the Yang-Baxter equation. They coincide with the previously known\(\hat R\)-matrices for SO q (3) and SO q (3, 1). Also, they are the three\(\hat R\)-matrices which can be constructed by using four different SU q (2) doublets. Only two of the three\(\hat R\)-matrices allow a differential structure on the reducible four-dimensional quantum space.
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Lorek, A., Schmidke, W.B. & Wess, J. SU q (2) covariant\(\hat R\)-matrices for reducible representations. Lett Math Phys 31, 279–288 (1994). https://doi.org/10.1007/BF00762790
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DOI: https://doi.org/10.1007/BF00762790