Abstract
In present paper we define a new kind of weak quantized enveloping algebra of Borcherds superalgebras. We denote this algebra by $wU_{q}^{\tau}(\mathcal{G})$ . It is a noncommutative and noncocommutative weak graded Hopf algebra under some additional condition. It has a homomorphic image which is isomorphic to the usual quantum enveloping algebra $U_{q}(\mathcal{G})$ of $\mathcal{G}$ .
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