Abstract
In this paper we study the G-identities for the Lie algebra sl2(C) over the complex field C. If sl2(C) is acted on faithfully by a finite group G then G is isomorphic to one of the following groups: Cn, Dn, A4, S4, A5. Here Cn is the cyclic group of order n, Dn is the dihedral group (of order 2n), An and Sn stand for the alternating and for the symmetric group permuting n letters, respectively.In each one of the above cases we describe a basis of the G-identities for sl2(C). In order to do that we use the explicit form of the graded identities for sl2(C) as well as properties of the group algebras of the corresponding groups. The same problem for the associative algebra M2(C) of the 2×2 matrices was settled by A. Berele in 2004.
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