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We study the double Yangian associated with the Lie superalgebra$\mathfrak{gl}_{m|n}$. Our main focus is on establishing thePoincar\'{e}-Birkhoff-Witt Theorem for the double Yangian and constructing itscentral elements in the form of coefficients of the quantum contraction. Next,as an application, we introduce reflection algebras, certain left coidealsubalgebras of the level 0 double Yangian, and find their presentations bygenerators and relations.

Double Yangian and reflection algebras of the Lie superalgebra $\mathfrak{gl}_{m|n}$