Terwilliger algebras of wreath products of association schemes

Mikhail Muzychuk; Bangteng Xu

doi:10.1016/j.laa.2015.11.030

Terwilliger algebras of wreath products of association schemes

Mikhail Muzychuk, Bangteng Xu

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

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 language	English
Pages (from-to)	146-163
Number of pages	18
Journal	Linear Algebra and Its Applications
Volume	493
DOIs	https://doi.org/10.1016/j.laa.2015.11.030
State	Published - 15 Mar 2016
Externally published	Yes

Keywords

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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10.1016/j.laa.2015.11.030

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title = "Terwilliger algebras of wreath products of association schemes",

abstract = "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.",

keywords = "Association schemes, Bose-Mesner algebras, Coherent configurations, Primitive central idempotents, Terwilliger algebras",

author = "Mikhail Muzychuk and Bangteng Xu",

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doi = "10.1016/j.laa.2015.11.030",

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T1 - Terwilliger algebras of wreath products of association schemes

AU - Muzychuk, Mikhail

AU - Xu, Bangteng

PY - 2016/3/15

Y1 - 2016/3/15

N2 - 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.

AB - 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.

KW - Association schemes

KW - Bose-Mesner algebras

KW - Coherent configurations

KW - Primitive central idempotents

KW - Terwilliger algebras

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U2 - 10.1016/j.laa.2015.11.030

DO - 10.1016/j.laa.2015.11.030

M3 - Article

AN - SCOPUS:84950284981

VL - 493

SP - 146

EP - 163

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

ER -

Terwilliger algebras of wreath products of association schemes

Abstract

Keywords

ASJC Scopus subject areas

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