AI 中文总结
本文通过拟阵理论分解Bestvina-Brady群的图同构问题，证明有限表示仅依赖循环拟阵，并构造高连通图使拟阵不同但群同构，且对偶弦图定义的BBG为右角Artin群。
AI 中文摘要
我们提出通过拟阵理论对Bestvina-Brady群（BBGs）的图同构问题进行分解。特别地，我们证明有限表示的BBGs仅通过其循环拟阵依赖于其定义图。另一方面，我们构造了任意高连通性的图，使得它们具有非同构的循环拟阵但它们的BBGs是同构的。为此，我们证明如果一个图允许树团生成子图，那么其BBG的Dicks-Leary表示可以显式简化为右角Artin群表示。特别地，我们证明由对偶弦图定义的BBGs是右角Artin群。
英文摘要
We propose a factorization of the graph isomorphism problem for Bestvina-Brady groups (BBGs) through matroid theory. In particular, we show that finitely presented BBGs depend on their defining graphs only through their cycle matroids. On the other hand, we construct graphs of arbitrarily high connectivity such that they have non-isomorphic cycle matroids but their BBGs are isomorphic. To do so, we prove that if a graph admits a tree clique-spanner, then the Dicks-Leary presentation of its BBG can be explicitly simplified to a right-angled Artin group presentation. In particular, we show that BBGs defined by dually chordal graphs are right-angled Artin groups.
Comments28 pages, 6 figures
