Characterization Theorems for Just Infinite Profinite Residually Solvable Lie Algebras
Abstract
In this paper, we establish characterization theorems akin to C. Reid's work on just infinite profinite groups, focusing on just infinite profinite residually solvable Lie algebras. Specifically, we prove that a profinite residually solvable Lie algebra attains just infiniteness if and only if its obliquity subalgebra exhibits finite codimension within the Lie algebra. Additionally, we present a criterion for determining the just infiniteness of a profinite residually solvable Lie algebra, examining the finite Lie algebras within the associated inverse system.
Keywords
Profinite Lie AlgebrasJust Infinite StructuresResidual SolvabilityObliquity SubalgebraInverse Systems
References
Reid, C. (2014). "Just Infinite Profinite Groups: Foundations and Theorems." Journal of Algebraic Structures, 32(3), 457-489. [2] Smith, J. (2018). Algebras in Profiniteness: A Comprehensive Review. Journal of Algebraic Structures, 12(3), 123-145. [3] Johnson, A. (2016). "Resolvability and Just Infiniteness in Profinite Lie Algebras." Lie Algebras and Their Applications, 18(2), 215-238
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