Data

"Nilpotent Lie algebras obtained by quivers and Ricci solitons", The 8th workshop “Complex Geometry and Lie Groups” (Osaka University Nakanoshima Center), 2025/03/13

Abstract

Nilpotent Lie groups with left-invariant metrics provide non-trivial examples of Ricci solitons. In this talk, we use quivers to construct nilpotent Lie algebras. A quiver is a directed graph that allows loops and multiple arrows between vertices. Utilizing the concept of paths within quivers, we introduce a method for constructing nilpotent Lie algebras from finite quivers without cycles. We prove that for all these Lie algebras, the corresponding simply-connected nilpotent Lie groups admit left-invariant Ricci solitons. The method we present constructs a broad family of Ricci soliton nilmanifolds with arbitrarily high degrees of nilpotency. Additionally, we mention some recent progress related to this topic. This work is based on collaboration with Fumika Mizoguchi.

Slide

Hiroshi Tamaru; Nilpotent Lie algebras obtained by quivers and Ricci solitons, 2025/03