# On Coherent Terwilliger Algebras and Wreath Products

**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.