Abstract
In this paper, we define a new type restricted quantum group Ūq(sl2*) and determine its Hopf Poincaré-Birkhoff-Witt-deformations Ūq(sl2*,κ) in which Ūq(sl2*,0)=Ūq(sl2*) and the classical restricted Drinfeld–Jimbo quantum group Ūq(sl2) is included. We show that Ūq(sl2*) is a basic Hopf algebra, then uniformly realize Ūq(sl2*) and Ūq(sl2) via some quotients of (deformed) preprojective algebras corresponding to the Gabriel quiver of Ūq(sl2*). Moreover, we obtain a uniform tensor-categorical realization of Ūq(sl2*) and Ūq(sl2), which is consistent with the above-mentioned Hopf-algebraic realization.
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