https://neckpinch.com/authors/fumika-mizoguchi/New arXiv papers by Fumika Mizoguchi, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2610.25883arxiv:2610.25883Mon, 19 Oct 2026 00:00:00 GMTFumika Mizoguchi — In the study of geometric structures on nilmanifolds, two-step nilpotent Lie algebras obtained by graphs play an important role. Recently, additional examples of nilpotent Lie algebras have been constructed from finite quivers without cycles. These latter examples can have arbitrarily high degrees of nilpotency, and admit Riemannian Ricci soliton metrics. In this paper, we study nilpotent Lie algebras obtained by finite quivers without cycles that are two-step nilpotent, and we prove that they can also be obtained by graphs. Using this relationship, we demonstrate that every two-step nilpotent Lie algebra obtained by a finite quiver without cycles admits a pseudo-Riemannian Ricci-flat metric. Additionally, we also classify these nilpotent Lie algebras that admit symplectic structures.Ricci solitonsRicci-flat & Calabi–YauHomogeneous spacesDiscrete & graph Ricci https://arxiv.org/abs/2607.06975arxiv:2607.06975Wed, 08 Jul 2026 00:00:00 GMTFumika Mizoguchi — In geometry, it is important to study whether a given Lie group admits a special left-invariant geometric structure. In our previous work, we constructed nilpotent Lie algebras from finite quivers without cycles by utilizing paths within these quivers. Also, we proved that the simply-connected Lie groups corresponding to these nilpotent Lie algebras always admit left-invariant Ricci solitons. In this paper, we extend our approach by constructing solvable Lie algebras from finite quivers without cycles, adding vertices as paths of length zero. We demonstrate that the simply-connected Lie groups corresponding to these solvable Lie algebras always admit left-invariant Ricci solitons. Moreover, we prove that when the quivers are oriented multi-trees, these Ricci soliton Lie groups are rigid, that is the direct product manifold of a flat manifold and an Einstein manifold.Ricci solitonsEinstein metricsHomogeneous spacesDiscrete & graph Ricci https://arxiv.org/abs/2405.11184arxiv:2405.11184Sat, 18 May 2024 00:00:00 GMTFumika Mizoguchi, Hiroshi Tamaru — Nilpotent Lie groups with left-invariant metrics provide non-trivial examples of Ricci solitons. One typical example is given by the class of two-step nilpotent Lie algebras obtained from simple directed graphs. In this paper, however, we focus on the use of quivers to construct nilpotent Lie algebras. A quiver is a directed graph that allows loops and multiple arrows between two 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 introduce constructs a broad family of Ricci soliton nilmanifolds with arbitrarily high degrees of nilpotency.Ricci solitonsHomogeneous spacesDiscrete & graph Ricci