# On Coherent Terwilliger Algebras and Wreath Products

### Misha Muzychuk Netanya Academic College

#### Bangteng Xu Eastern Kentucky University

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Minisymposium: ASSOCIATION SCHEMES

Content: Let $\mathcal{A}\subseteq M_\Omega[\mathbb{F}]$ be a coherent algebra. It's Terwilliger algebra $\mathcal{T}_\omega (\mathcal{A})$ is called {\it coherent} if $\mathcal{T}_\omega$ is closed with respect to Schur-Hadamard product. In our talk we'll present some properties of coherent Terwilliger algebra. We also present a theorem which provides a complete description of T-algebra of a wreath product of association schemes. Using this result we prove that if both factors of the wreath product have coherent T-algebras, then the wreath product has a coherent T-algebra too.

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