Examples of Self-Iterating Lie Algebras, 2 (original) (raw)

v1 = ∂1 + t0(∂2 + t1(∂3 + t2(∂4 + t3(∂5 + t4(∂6 + · · · ))))); v2 = ∂2 + t1(∂3 + t2(∂4 + t3(∂5 + t4(∂6 + · · · )))). Let L = Liep(v1, v2) ⊂ DerR be the restricted Lie algebra generated by these derivations. We establish the following properties of this algebra in case p = 2, 3. a) L has a polynomial growth with Gelfand-Kirillov dimension ln p/ ln((1+ √ 5)/2). b) the associative envelope A = Alg(v1, v2) of L has Gelfand-Kirillov dimension 2 ln p/ ln((1+ √ 5)/2). c) L has a nil-p-mapping. d) L , A and the augmentation ideal of the restricted enveloping algebra u = u0(L) are direct sums of two locally nilpotent subalgebras. The question whether u is a nil-algebra remains open. e) the restricted enveloping algebra u(L) is of intermediate growth. These properties resemble those of Grigorchuk and Gupta-Sidki groups. Mathematics Subject Classification 2000: 17B05, 17B50, 17B66, 16P90, 11B39.