代数与表示论讨论班

Title: On triprojective dg algebras

Speaker: Professor Bernhard Keller/孔博恩 (Universite Paris Cite/巴黎西岱大学)

Time: 9:30-10:30pm, Dec. 8 (Monday), 2025

Place: 数学科学学院(紫金港校区海纳苑2幢) 202室

Abstract:

For a Dynkin quiver Q, the triprojective (dg) algebra associated

with Q is glued together from three copies of the corresponding

preprojective (dg) algebra. The category of Gorenstein projective dg modules over the

triprojective dg algebra is expected to categorify Goncharov-Shen's

cluster variety of triples of flags of the type of Q and this is our main motivation for considering them. Our aims in these lectures are to

1) construct the triprojective (dg) algebra as the boundary dg algebra

(in the sense of Yilin Wu) associated with a relative 3-Calabi-Yau

completion and

2) sketch the construction of the expected symmetries of the

(derived category of) its category of Gorenstein projective dg modules:

an action of the cyclic group of order 6 and an action of the

twist-invariant braid group of the type of Q.

This is a report on joint work with Miantao Liu and with Zhenhui Ding.