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Let $k_q[x, x^{-1}, y]$ be the localization of the quantum plane $k_q[x, y]$over a field $k$, where $0\neq q\in k$. Then $k_q[x, x^{-1}, y]$ is a gradedHopf algebra, which can be regarded as the non-negative part of the quantumenveloping algebra $U_q({\mathfrak sl}_2)$. Under the assumption that $q$ isnot a root of unity, we investigate the coalgebra automorphism group of $k_q[x,x^{-1}, y]$. We describe the structures of the graded coalgebra automorphismgroup and the coalgebra automorphism group of $k_q[x, x^{-1}, y]$,respectively.

The Coalgebra Automorphism Group of Hopf Algebra $k_q[x, x^{-1}, y]$