Pseudo-direct Sums and Wreath Products of Loose-coherent Algebras with Applications to Coherent Configurations

Department

Business

Department Name When Scholarship Produced

Mathematics and Statistics

Document Type

Article

Publication Date

10-2017

Abstract

We introduce the notion of a loose-coherent algebra, which is a special semisimple subalgebra of the matrix algebra, and define two operations to obtain new loose-coherent algebras from the old ones: the pseudo-direct sum and the wreath product. For two arbitrary coherent configurations C" role="presentation">, D" role="presentation"> and their wreath product C≀D" role="presentation">, it is difficult to express the Terwilliger algebra T(x,y)(C≀D)" role="presentation"> in terms of the Terwilliger algebras Tx(C)" role="presentation"> and Ty(D)" role="presentation">. By using the concept and operations of loose-coherent algebras, we find a very simple such expression. As a direct consequence of this expression, we obtain the central primitive idempotents of T(x,y)(C≀D)" role="presentation"> in terms of the central primitive idempotents of Tx(C)" role="presentation"> and Ty(D)" role="presentation">. Many results in[4,6,10,12] are special cases of the results in this paper.

Journal Title

Linear Algebra and Its Applications

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