Abstract
A relation between q-oscillator R-matrix of the tetrahedron equation and decompositions of Poinkaré–Birkhoff–Witt type bases for nilpotent subalgebras \({\fancyscript{U}}_q({\mathfrak{n}}_+)\subset{\fancyscript{U}}_q(sl_n)\) is observed.
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References
Bazhanov V.V. and Sergeev S.M. (2006). Zamolodchikov’s tetrahedron equation and hidden structure of quantum groups. J. Phys. A 39: 3295–3310
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Sergeev, S.M. Tetrahedron Equations and Nilpotent Subalgebras of \({\fancyscript{U}}_q(sl_n)\) . Lett Math Phys 83, 231–235 (2008). https://doi.org/10.1007/s11005-008-0219-x
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DOI: https://doi.org/10.1007/s11005-008-0219-x