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Profinite just infinite residually solvable Lie algebras | ||
| International Journal of Group Theory | ||
| مقاله 4، دوره 12، شماره 4، اسفند 2023، صفحه 253-264 اصل مقاله (392.73 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2022.130053.1734 | ||
| نویسنده | ||
| Dario Villanis Ziani* | ||
| Department of Mathematics and Computer Science “U. Dini”, Università degli Studi di Firenze, viale Morgagni 67/A, 50134, Florence, Italy | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| just-infinite Lie algebras؛ profinite Lie algebras؛ residually solvable Lie algebras | ||
| مراجع | ||
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[1] C. D. Reid, On the structure of just infinite profinite groups, J. Algebra, 324 (2010) 2249–2261. [2] C. D. Reid, Inverse system characterizations of the (hereditarily) just infinite property in profinite groups, Bull. Lond. Math. Soc., 44 (2012) 413-425. | ||
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