Split bases for quantum cluster algebras associated with triangular extensions
数学专题报告
报告题目(Title)：Split bases for quantum cluster algebras associated with triangular extensions
报告人(Speaker)：王茂鹏（北京师范大学）
地点(Place)：后主楼1220
时间(Time)：2026年6月3日（周三）16:00-16:55
邀请人(Inviter)：肖杰、覃帆、周宇
报告摘要
In this talk, I will present a basis construction for quantum cluster algebras associated with triangular extensions and admitting the common triangular basis. For such an algebra, we construct a new basis, called the split basis, whose elements are normalized ordered products of basis elements coming from the smaller pieces of the triangular extension. We prove that the split basis is a PBW-type basis, and that the common triangular basis is obtained from it by a Kazhdan–Lusztig-type unitriangular transition. In this sense, the construction exhibits a cluster-algebraic analogue of the relationship between the dual PBW basis and the dual canonical basis. This is a joint work with Fan Qin.
