Terwilliger algebras of wreath products of association schemes

Mikhail Muzychuk, Bangteng Xu

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


The Terwilliger algebra of an association scheme of order n introduced in [13] is a subalgebra of the matrix algebra of all n×n matrices. Terwilliger algebras of wreath products of special association schemes are studied in several papers. In this paper we study the Terwilliger algebra of the wreath product T|S of two arbitrary association schemes S and T. We will express the Terwilliger algebra of T|S and its primitive central idempotents in terms of the Terwilliger algebras of S and T and their primitive central idempotents. The known results of Hanaki, Kim, etc. (cf. [7,10]) are special cases of our results.

Original languageEnglish
Pages (from-to)146-163
Number of pages18
JournalLinear Algebra and Its Applications
StatePublished - 15 Mar 2016
Externally publishedYes


  • Association schemes
  • Bose-Mesner algebras
  • Coherent configurations
  • Primitive central idempotents
  • Terwilliger algebras

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics


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