The real forms of the S_3-graded algebras sl(2,C)

Obtaining real forms of complex Lie algebras (or complex Lie groups) is important in mathematical physics and engineering applications.One of these Lie algebras is the Lie algebra sl(2, C) and its real forms.In our study, we obtain the S 3 -graded algebras sl(2, R) which are the real forms of the S 3 -graded algebras sl(2, C) for dimensional matrix representations M =1, 2, 3 and 4.