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

Let k(q)[x, x(-1), y] be the localization of the quantum plane k(q)[x, y] over a field k, where 0 not equal q is an element of k. Then k(q)[x, x(-1), y] is a graded Hopf algebra, which can be regarded as the non-negative part of the quantum enveloping algebra U-q(sl(2)). Under the assumption that q is not 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 automorphism group and the coalgebra automorphism group of k(q)[x, x(-1), y], respectively. (C) 2013 Elsevier B.V. All rights reserved.