Profinite just infinite residually solvable Lie algebras

Document Type : Research Paper


Department of Mathematics and Computer Science “U. Dini”, Università degli Studi di Firenze, viale Morgagni 67/A, 50134, Florence, Italy


We provide some characterization theorems about just infinite profinite residually solvable Lie algebras, similarly to what C. Reid has done for just infinite profinite groups. In particular, we prove that a profinite residually solvable Lie algebra is just infinite if and only if its obliquity subalgebra has finite codimension in the Lie algebra, and we establish a criterion for a profinite residually solvable Lie algebra to be just infinite, looking at the finite Lie algebras occurring in the inverse system.


Main Subjects

[1] C. D. Reid, On the structure of just infinite profinite groups, J. Algebra, 324 (2010) 2249–2261.
[2] C. D. Reid, Inverse system characterizations of the (hereditarily) just infinite property in profinite groups, Bull.
Lond. Math. Soc., 44 (2012) 413-425.