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Quantisation ideals, canonical parametrisations of the unipotent group and consistent integrable systems
M. A. Chirkov, A. V. Mikhailov, D. V. Talalaev
https://arxiv.org/abs/2505.20253

Quantisation ideals, canonical parametrisations of the unipotent group and consistent integrable systems
Using the methods of quantisation ideals, we construct a family of quantisations corresponding to Case alpha in Sergeev's classification of solutions to the tetrahedron equation. This solution describes transformations between special parametrisations of the space of unipotent matrices with noncommutative coefficients. We analyse the classical limit of this family and construct a pencil of compatible Poisson brackets that remain invariant under the re-parametrisation maps (mutations). This deco…