A non-Hermitian spin chain that fails ordinary Yang-Baxter integrability still possesses a hidden staggered nilpotent symmetry generated by a cross-commuting scalene transfer matrix.
Integrability test for spin chains,
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Scalene Yang--Baxter triples as a source of hidden symmetries beyond the ordinary Yang--Baxter equation
A non-Hermitian spin chain that fails ordinary Yang-Baxter integrability still possesses a hidden staggered nilpotent symmetry generated by a cross-commuting scalene transfer matrix.