Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5776974 | Discrete Mathematics | 2017 | 14 Pages |
Abstract
We introduce the notion of the combinatorial extension of a Terwilliger algebra by a coherent algebra. By using this notion, we find a simple way to describe the Terwilliger algebras of certain coherent configurations as combinatorial extensions of simpler Terwilliger algebras. In particular, given an association scheme S and another association scheme R such that the Terwilliger algebra of R is isomorphic to a coherent algebra, we prove that the Terwilliger algebra of the wreath product SâR is isomorphic to the combinatorial extension of the Terwilliger algebra of S by a coherent algebra. We also show that the Terwilliger algebra of the wreath product W of rank 2 association schemes can be expressed as the combinatorial extension of adjacency algebras of association schemes induced by the closed subsets of W. As a direct consequence, we obtain simple conceptual explanations and alternative proofs of many known results on the structures of Terwilliger algebras of wreath products of association schemes.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Sung Y. Song, Bangteng Xu, Shenglin Zhou,