You are here: Seminars > 2024 > November 20th

The Terwilliger algebras of the group association schemes of non-abelian finite groups admitting an abelian subgroup of index 2

杨靖 Jing Yang

Central South University

Time: 16:00-17:00 (GMT+8), Wednesday November 20th, 2024
Location: Zoom


Abstract: For any finite group \(G\), the Terwilliger algebra \(\mathcal{T}(G)\) of the group association scheme satisfies the following inclusions: \(\mathcal{T}_0(G)\subseteq \mathcal{T}(G)\subseteq\widetilde{\mathcal{T}}(G)\), where \(\mathcal{T}_0(G)\) is a specific vector space and \(\widetilde{\mathcal{T}}(G)\) is the centralizer algebra of the permutation representation of \(G\) induced by the action of conjugation. The group \(G\) is said to be triply transitive if \(\mathcal{T}_0(G)=\widetilde{\mathcal{T}}(G)\).In this paper, we determine the dimension of the Terwilliger algebras of non-abelian finite groups admitting an abelian subgroup of index 2 by showing that they are triply transitive. Moreover, we give a complete characterization of the Wedderburn components of the Terwilliger algebras of these groups.


Host: 陈俊彦 Junyan Chen

Slides