Speaker：Peigen Cao (University of Science and Technology of China)

Time：2025-11-29 16:00

Location：Conference Room S106 at Experiment Building at Haiyun Campus

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.