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

Hui-Xiang Chen

• Let kq[x, x.1, y] be the localization of the quantum plane kq[x, y] over a field k, where 0 .= q ¡ô k. Then kq[x, x.1, y] is a graded Hopf algebra, which can be regarded as the nonnegative 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.