The coalgebra automorphism group of Hopf algebra kq[x,x−1,y]

Let kq[x,x−1,y] be the localization of the quantum plane kq[x,y] over a field k, where 0≠q∈k. Then kq[x,x−1,y] is a graded Hopf algebra, which can be regarded as the non-negative part of the quantum enveloping algebra Uq(sl2). Under the assumption that q is not a root of unity, we investigate the coalgebra automorphism group of kq[x,x−1,y]. We describe the structures of the graded coalgebra automorphism group and the coalgebra automorphism group of kq[x,x−1,y], respectively.