【代数与表示论讨论班】Λ-invariant and tropical invariant in cluster theory

Speaker: 曹培根 教授（中国科学技术大学)

Time: 10:10-11:10am, Dec. 8 (Monday), 2025

Place: 数学科学学院(紫金港校区海纳苑2幢) 202室

 Abstract: The Λ-invariant and d-invariant are introduced by Kang-Kashiwara-Kim-Oh and by Kashiwara-Kim-Oh-Park in the study of monoidal cluster categorification using finite-dimensional modules over quiver Hecke algebras and quantum affine algebras. It is known that many interesting cluster algebras carry a natural compatible Poisson structure. Such cluster algebras are called Λ-cluster algebras. The Λ-invariant can be viewed as the monoidal categorification of the compatible Poisson structure but it contains much more information. 

The tropical invariant and F-invariant for a pair of good elements (e.g., cluster monomials) in a Λ-cluster algebra are introduced in my paper. It is proved that the Λ-invariant coincides with the tropical invariant on cluster monomials and hence the twice d-invariant coincides with the F-invariant.