RESIDUALLY SOLVABLE JUST INFINITE PROFINITE LIE ALGEBRAS

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Villanis Ziani Dario

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Journal Paper

Paper Information

Journal: INTERNATIONAL JOURNAL OF GROUP THEORY Year:2023 | Volume:12 | Issue:4 Page(s): 253-264

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Information Journal Paper

Title

RESIDUALLY SOLVABLE JUST INFINITE PROFINITE LIE ALGEBRAS

Author(s)

Villanis Ziani Dario | Issue Writer Certificate

Keywords

profinite Lie algebras

just infinite Lie algebras

residually solvable Lie algebras

Abstract

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.

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