arXiv subjects

Xueqin Hu

Publications and source records attributed to Xueqin Hu.

4 recordsLinked to original sources

arXiv2026

Hyperfocal subalgebras of hyperfocal abelian Frobenius blocks

In this paper, we introduce a class of blocks which is called hyperfocal abelian Frobenius blocks.This class of blocks is an analogous version of the block with abelian defect group and Frobenius inertial quotient at hyperfocal level and includes the blocks with Klein four hyperfocal subgroups and cyclic hyperfocal subgroups. We show that there is a stable equivalence of Morita type between the hyperfocal subalgebras of the hyperfocal abelian Frobenius blocks and a group algebra of a Frobenius group associated with the hyperfocal subgroup of the block. As applications, we can partially describe some structures of the blocks with Klein four hyperfocal subgroups and cyclic hyperfocal subgroups,such as the structures of their hyperfocal subalgebras in terms of derived categories and the structures of their characters. As a consequence, we show that Broue's abelian defect group conjecture holds for blocks with Klein four hyperfocal subgroups.

math.GR↗

arXiv2025

Spatiotemporal Graph Learning with Direct Volumetric Information Passing and Feature Enhancement

Data-driven learning of physical systems has kindled significant attention, where many neural models have been developed. In particular, mesh-based graph neural networks (GNNs) have demonstrated significant potential in modeling spatiotemporal dynamics across arbitrary geometric domains. However, the existing node-edge message-passing and aggregation mechanism in GNNs limits the representation learning ability. In this paper, we proposed a dual-module framework, Cell-embedded and Feature-enhanced Graph Neural Network (aka, CeFeGNN), for learning spatiotemporal dynamics. Specifically, we embed learnable cell attributions to the common node-edge message passing process, which better captures the spatial dependency of regional features. Such a strategy essentially upgrades the local aggregation scheme from first order (e.g., from edge to node) to a higher order (e.g., from volume and edge to node), which takes advantage of volumetric information in message passing. Meanwhile, a novel feature-enhanced block is designed to further improve the model's performance and alleviate the over-smoothness problem. Extensive experiments on various PDE systems and one real-world dataset demonstrate that CeFeGNN achieves superior performance compared with other baselines.

cs.LG↗

arXiv2019

Blocks with abelian defect groups of rank 2 and one simple module

In this paper, we investigate the block that has an abelian defect group of rank $2$ and its Brauer correspondent has only one simple module. We will get an isotypy between the block and its Brauer correspondent. It will generalize the result of Kessar and Linckelmann (\cite{KL}).

math.GR↗

arXiv2018

Blocks with the hyperfocal subgroup $Z_{2^n}\times Z_{2^n}$

In this paper, we calculate the numbers of irreducible ordinary characters and irreducible Brauer characters in a block of a finite group $G$, whose associated fusion system over a 2-subgroup $P$ of $G$ (which is a defect group of the block) has the hyperfocal subgroup $\mathbb Z_{2^n}\times \mathbb Z_{2^n}$ for some $n\geq 2$, when the block is controlled by the normalizer $N_G(P)$ and the hyperfocal subgroup is contained in the center of $P$, or when the block is not controlled by $N_G(P)$ and the hyperfocal subgroup is contained in the center of the unique essential subgroup in the fusion system. In particular, Alperin's weight conjecture holds in the considered cases.

math.GR↗