Let L be a restricted Lie algebra over a field of characteristic p>0. We investigate the structure of L when its lattice S(L) of restricted subalgebras satisfies some prescribed properties. In particular, we establish when S(L) is distributive. The special form that this result takes when F is either the field with p elements or an algebraically closed field is also discussed. Furthermore, we establish when S(L) is Boolean or the two-elements lattice.
Restricted Lie algebras having a distributive lattice of restricted subalgebras
MALETESTA, NICOLAMembro del Collaboration Group
;Salvatore Siciliano
Membro del Collaboration Group
2021-01-01
Abstract
Let L be a restricted Lie algebra over a field of characteristic p>0. We investigate the structure of L when its lattice S(L) of restricted subalgebras satisfies some prescribed properties. In particular, we establish when S(L) is distributive. The special form that this result takes when F is either the field with p elements or an algebraically closed field is also discussed. Furthermore, we establish when S(L) is Boolean or the two-elements lattice.File in questo prodotto:
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