The Lie algebra sl2(K) over a field K has a natural grading by 2, the cyclic group of order 2. We describe the graded polynomial identities for this grading when the base field 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 sl2(K) graded by other groups such as 2 × 2, and by the integers . © 2008 World Scientific Publishing Company.185825836Azevedo, S.S., Graded identities for the matrix algebra of order n over an infinite field (2002) Commun. Algebra, 30 (12), pp. 5849-5860Azevedo, S.S., A basis for ℤ-graded identities of matrices over infinite fields (2003) Serdica, 29, pp. 149-158Colombo, J., Koshlukov, P., Central polynomials in the matrix algebra of order two (2004) Linear Algebra Appl, 377, pp. 53-67De Concini, C., Procesi, C., A characteristic free approach to invariant theory (1976) Adv. Math, 21 (3), pp. 330-354Di Vincenzo, O.M., On the graded identities of M 1,1(E) (1992) Israel J. Math, 80 (3), pp. 323-335Drensky, V., (1999) Free Algebras and PI Algebras, Graduate Course in Algebra, , Springer, SingaporeKoshlukov, P., Weak polynomial identities for the matrix algebra of order two (1997) J. Algebra, 188 (2), pp. 610-625Koshlukov, P., Basis of the identities of the matrix algebra of order two over a field of characteristic p2 (2001) J. Algebra, 241, pp. 410-434Koshlukov, P., Azevedo, S.S., Graded identities for T-prime algebras over fields of positive characteristic (2002) Israel J. Math, 128, pp. 157-176Koshlukov, P., Krasilnikov, A., Just nonfinitely based varieties of 2-graded Lie algebras submittedRazmyslov, Y., Identities of Algebras and Their Representations, Translations Math (1994) Monographs, 138. , American Mathematical Society, Providence, RIRepin, D.V., Graded identities of a simple three-dimensional Lie algebra (2004) Vestn. Samar. Gos. Univ. Estestvennonauchn. Ser, (SPEC. ISSUE 2), pp. 5-16. , in RussianRepin, D.V., (2005) Structure and identities of some graded Lie algebras, , PhD thesis, Ulyanovsk State University, Ulyanovsk , in RussianVasilovsky, S.Y., graded polynomial identities of the full matrix algebra (1998) Commun. Algebra, 26 (2), pp. 601-612. , ℤVasilovsky, S.Y., n-graded polynomial identities of the full matrix algebra of order n (1999) Proc. Amer. Math. Soc, 127 (12), pp. 3517-3524. , ℤVasilovsky, S., The basis of identities of a three-dimensional simple Lie algebra over an infinite field (1989) Algebra Logic, 28 (5), pp. 355-368