Feigin, B.Jimbo, M.Mukhin, E.2024-12-192024-12-192024-06Feigin, B., Jimbo, M., & Mukhin, E. (2024). Commutative subalgebra of a shuffle algebra associated with quantum toroidal glm|n. Journal of Pure and Applied Algebra, 228(6), 107619. https://doi.org/10.1016/j.jpaa.2024.107619https://hdl.handle.net/1805/45136We define and study the shuffle algebra Shm|n of the quantum toroidal algebra Em|n associated to Lie superalgebra glm|n. We show that Shm|n contains a family of commutative subalgebras Bm|n(s) depending on parameters s=(s1,…,sm+n), ∏isi=1, given by appropriate regularity conditions. We show that Bm|n(s) is a free polynomial algebra and give explicit generators which conjecturally correspond to the traces of the s-weighted R-matrix computed on the degree zero part of Em|n modules of levels ±1.enPublisher Policymathematicsquantum algebramathematical physicsArticle