Outer Automorphisms of Lie Algebras related with Generic 2×2 Matrices
2010 Mathematics Subject Classification: 17B01, 17B30, 17B40, 16R30. Let Fm = Fm(var(sl2(K))) be the relatively free algebra of rank m in the variety of Lie algebras generated by the algebra sl2(K) over a field K of characteristic 0. Our results are more precise for m = 2 when F2 is isomorphic to the Lie algebra L generated by two generic traceless 2 × 2 matrices. We give a complete description of the group of outer automorphisms of the completion L^ of L with respect to the formal power...