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arXiv · 2201.01718

On the subalgebra lattice of a restricted Lie algebra]{On the subalgebra lattice of a restricted Lie algebra

Pilar Paez-Guillan·Salvatore Siciliano·David A. Towers
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Abstract

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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Pilar Paez-Guillan, Salvatore Siciliano, David A. Towers. 2022-01-05. On the subalgebra lattice of a restricted Lie algebra]{On the subalgebra lattice of a restricted Lie algebra. https://arxiv.org/abs/2201.01718

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