Additive categorification of the monoidal Lambda-invariantOberseminar Algebra und Darstellungstheorie

by Ricardo Canesin (Université Paris Cité)

Wednesday May 13, 2026, 6:00 PM → 7:00 PM Europe/Berlin

Endenicher Allee 60/0-008 - Seminarraum (Mathezentrum)

The Lambda-invariant for quantum affine algebras was introduced by Kashiwara-Kim-Oh-Park as an important tool in their study of the monoidal categorification of cluster algebras. It yields a quantization of the associated cluster algebra, and it was recently shown to coincide with Peigen Cao’s tropical invariant.

In this talk, we interpret these invariants via the additive categorification of cluster algebras using Higgs categories in the sense of Yilin Wu. Whenever the relative Ginzburg algebra is proper, we show that the Higgs category admits a canonical quantum structure generalizing those of Geiss-Leclerc-Schröer and Grabowski-Pressland, and we provide a homological interpretation of the corresponding tropical invariant.

 

For certain finite-rank cluster algebras categorified by Kashiwara-Kim-Oh-Park, we show that the associated relative Ginzburg algebra is indeed proper, and that our additive Lambda-invariant agrees with their monoidal one.

This is joint work with Peigen Cao and Geoffrey Janssens.