IIARD International Institute of Academic Research and Development

INTERNATIONAL JOURNAL OF COMPUTER SCIENCE AND MATHEMATICAL THEORY (IJCSMT )

E-ISSN 2545-5699
P-ISSN 2695-1924
VOL. 9 NO. 5 2023

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Characterization Theorems for Just Infinite Profinite Residually Solvable Lie Algebras

Michael N. John, Ogoegbulem Ozioma, Etim, Uduak James, Udoaka Otobong. G.

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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

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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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