University of IsfahanInternational Journal of Group Theory2251-765012420231201Profinite just infinite residually solvable Lie algebras2532642677210.22108/ijgt.2022.130053.1734ENDarioVillanis ZianiDepartment of Mathematics and Computer Science “U. Dini”, Università degli Studi di Firenze, viale Morgagni 67/A,
50134, Florence, Italy0000-0001-7826-2463Journal Article20210814We 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.https://ijgt.ui.ac.ir/article_26772_2b33a31566f445730af689d7f9c7233b.pdf