Embeddability of right-angled Artin groups on complements of trees

作者：Lee Eon Kyung^*; Lee Sang Jin

来源：International Journal of Algebra and Computation, 2018, 28(3): 381-394.

DOI：10.1142/S0218196718500182

• Right-anglexl Artin groups
• extension graphs
• embeddability

For a finite simplicial graph Gamma, let A(Gamma) denote the right-angled Artin group on Gamma. Recently, Kim and Koberda introduced the extension graph Gamma(e) for Gamma, and established the Extension Graph Theorem: for finite simplicial graphs Gamma(1) and Gamma(2), if Gamma(1) embeds into Gamma(e)(2) as an induced subgraph then A(Gamma(1)) embeds into A(Gamma(2)). In this paper, we show that the converse of this theorem does not hold for the case Gamma(1) is the complement of a tree and for the case Gamma(2) is the complement of a path graph.

• 出版日期2018-5