Characterization Theorems for Just Infinite Profinite Residually Solvable Lie Algebras
Michael N. John, Ogoegbulem Ozioma, Etim, Uduak James, Udoaka Otobong. G.
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 Algebras
Just Infinite Structures
Residual Solvability
Obliquity Subalgebra
Inverse 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
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
