Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)The Lie algebra sl(2)( K) over a field K has a natural grading by Z(2), the cyclic group of order 2. We describe the graded polynomial identities for this grading when the base. eld is infinite and of characteristic different from 2. We exhibit a basis of these identities that consists of one polynomial. In order to obtain this basis we employ methods and results from Invariant theory. As a by-product we obtain finite bases of the graded identities for sl(2)( K) graded by other groups such as Z(2) x Z(2), and by the integers Z.185825836Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)CNPq [302655/2005-0]FAPESP [2004/13766-2, 2005/60337-2]