Terwilliger algebras of wreath products of one-class association schemes
نویسندگان
چکیده
In this paper, we study the wreath product of one-class association schemes Kn =H(1, n) for n≥ 2. We show that the d-class association scheme Kn1 Kn2 · · · Knd formed by taking the wreath product of Kni (for ni ≥ 2) has the triple-regularity property. Then based on this fact, we determine the structure of the Terwilliger algebra of Kn1 Kn2 · · · Knd by studying its irreducible modules. In particular, we show that every non-primary module of this algebra is 1-dimensional.
منابع مشابه
Terwilliger algebras of wreath products of association schemes
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi CHAPTER 1. A GENERAL OVERVIEW AND INTRODUCTION . . . . 1 CHAPTER 2. PRELIMINARIES: COMMUTATIVE ASSOCIATION SCHEMES AND THEIR TERWILLIGER ALGEBRAS . . . . . . . . . . . . . . . . . 4 2.1 The Bose-Mesner Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 The Dual Bose-Mesner Algebra . . . . . . ....
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