arXiv subjects

Zhanhong Liang

Publications and source records attributed to Zhanhong Liang.

4 recordsLinked to original sources

arXiv2026

Are cluster automorphism groups finitely generated?

This paper investigates the finite generation of cluster automorphism groups. By applying the pseudo $\mathbb{N}$-grading introduced in our previous work, we establish a sufficient condition for a cluster automorphism group to be finitely generated. As applications, we re-establish the finite generation of the automorphism groups for all finite mutation type cluster algebras, and verify the acyclic cases. Furthermore, we illustrate through examples that our approach significantly simplifies the computation of presentations for these groups in certain cases.

math.RA↗

arXiv2026

GIM and Elliptic Lie algebras via Ringel--Hall Lie algebras

For any symmetrizable generalized intersection matrix (GIM) $C$, we construct an acyclic valued quiver $(Q,\mathbf{d})$ endowed with an involution $θ$. Let $\mathcal{D}$ be the bounded derived category of finite-dimensional representations of $(Q,\mathbf{d})$, and let $Σ$ stand for the suspension functor of $\mathcal{D}$. We show that the orbit category $\mathcal{D}/(θ\circΣ)$ carries a canonical triangulated structure and is $2$-periodic. Applying Peng--Xiao's construction to this orbit category, we prove that the GIM algebra $\operatorname{gim}(C)$ is isomorphic to the integral Ringel--Hall Lie algebra associated with $\mathcal{D}/(θ\circΣ)$. As a further application of the above machinery, we investigate elliptic Lie algebras of types $D_4^{(1,1)}$, $E_6^{(1,1)}$, $E_7^{(1,1)}$ and $E_8^{(1,1)}$. For each elliptic Dynkin diagram, we define a finite-dimensional algebra $A$ by taking an appropriate quotient of the acyclic quiver $Q$ attached to the GIM matrix $C$. From the resulting $2$-periodic triangulated categories, we build the corresponding Ringel--Hall Lie algebras, and establish a surjective Lie algebra homomorphism from each elliptic Lie algebra to its integral Ringel--Hall counterpart. This map is conjectured to be injective, and its injectivity on real root spaces is confirmed.

math.RT↗

arXiv2025

DASP: Self-supervised Nighttime Monocular Depth Estimation with Domain Adaptation of Spatiotemporal Priors

Self-supervised monocular depth estimation has achieved notable success under daytime conditions. However, its performance deteriorates markedly at night due to low visibility and varying illumination, e.g., insufficient light causes textureless areas, and moving objects bring blurry regions. To this end, we propose a self-supervised framework named DASP that leverages spatiotemporal priors for nighttime depth estimation. Specifically, DASP consists of an adversarial branch for extracting spatiotemporal priors and a self-supervised branch for learning. In the adversarial branch, we first design an adversarial network where the discriminator is composed of four devised spatiotemporal priors learning blocks (SPLB) to exploit the daytime priors. In particular, the SPLB contains a spatial-based temporal learning module (STLM) that uses orthogonal differencing to extract motion-related variations along the time axis and an axial spatial learning module (ASLM) that adopts local asymmetric convolutions with global axial attention to capture the multiscale structural information. By combining STLM and ASLM, our model can acquire sufficient spatiotemporal features to restore textureless areas and estimate the blurry regions caused by dynamic objects. In the self-supervised branch, we propose a 3D consistency projection loss to bilaterally project the target frame and source frame into a shared 3D space, and calculate the 3D discrepancy between the two projected frames as a loss to optimize the 3D structural consistency and daytime priors. Extensive experiments on the Oxford RobotCar and nuScenes datasets demonstrate that our approach achieves state-of-the-art performance for nighttime depth estimation. Ablation studies further validate the effectiveness of each component.

cs.CV↗

arXiv2025

Pseudo grading on cluster automorphism group with application to cluster algebras of rank $3$

We introduce a pseudo $\mathbb{N}$-grading on the cluster auotmorphism group $\operatorname{Aut}(\mathcal{A})$ with respect to an initial seed of $\mathcal{A}$, which consists of a family of subsets $\{G_i\}_{i\in \mathbb{N}}$ of $\operatorname{Aut}(\mathcal{A})$ such that $\operatorname{Aut}(\mathcal{A})=\bigcup_{i\in \mathbb{N}}G_i$ and $G_k\cdot G_l\subset \bigcup_{i=0}^{k+l}G_i$. We prove that $\operatorname{Aut}(\mathcal{A})$ is generated by $G_0\cup G_1$, leading to an elementary approach for calculating cluster automorphism groups of certain cluster algebras. As an application, we completely determined the cluster automorphism groups of cluster algebras of rank $3$ with indecomposable exchange matrices.

math.RA↗