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math.QA2025
Quantum symmetric pairs via Hall algebras
Ming Lu, Zhuoyi Zhao
A quantum symmetric pair consists of a quantum group and its coideal subalgebra . The Hall algebra constructions of $\wideti…
math.QA2025
iQuantum groups and iHopf algebras I: foundation
Jiayi Chen, Ming Lu, Xiaolong Pan +2
We introduce the notion of iHopf algebra, a new associative algebra structure defined on a Hopf algebra equipped with a Hopf pairing. The iHopf algebra on a Borel quantum group end…
math.QA2025
Dual canonical bases of quantum groups and quantum groups I: Hall algebras
Ming Lu, Xiaolong Pan
The quantum groups have two realizations: one via the Hall algebras and the other via the quantum Grothendieck rings of quiver varieties, as developed by the first…