On the subalgebra lattice of a restricted Lie algebra

Towers, Pilar Paez-Guillan and Towers, Salvatore Siciliano and Towers, David (2023) On the subalgebra lattice of a restricted Lie algebra. Linear Algebra and its Applications, 660. pp. 47-65. ISSN 0024-3795

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In this paper we study the lattice of restricted subalgebras of a restricted Lie algebra. In particular, we consider those algebras in which this lattice is dually atomistic, lower or upper semimodular, or in which every restricted subalgebra is a quasi-ideal. The fact that there are one-dimensional subalgebras which are not restricted results in some of these conditions being weaker than for the corresponding conditions in the non-restricted case.

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Journal Article
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Linear Algebra and its Applications
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21 Dec 2022 16:40
Last Modified:
16 Jan 2023 01:54