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We study the algebraic structures which govern the deformation ofsupersymmetric intersections of M2 and M5 branes. The universal algebras on M2and M5 branes are deformed double current algebra of $\mathfrak{gl}_K$ and$\mathfrak{gl}_K$-extended $\mathcal{W}_{\infty}$-algebra respectively. We givea new presentation of the deformed double current algebra of $\mathfrak{gl}_K$,and we give a rigorous mathematical construction of the$\mathfrak{gl}_K$-extended $\mathcal{W}_{\infty}$-algebra. A new presentationof the affine Yangian of $\mathfrak{gl}_K$ is also obtained. We constructvarious coproducts of these algebras, which are expected to encode the fusionsof defects in twisted M-theory. The matrix extended Miura operators areidentified as intertwiners in certain bimodules of these algebras.

Deformed Double Current Algebras, Matrix Extended $\mathcal W_{\infty}$ Algebras, Coproducts, and Intertwiners from the M2-M5 Intersection