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Uncountably Many Nonisomorphic Nilpotent Lie Algebras

1962
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Proceedings of the American Mathematical Society
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Throughout this note, L denotes a Lie algebra over the real number field R. We shall define L* and L, inductively. L = L° = L0, Li = [L*-1,1/-1], and L,= [L, Lv_i] for all integers *2ï 1. Thus, L* is the space of all finite sumsEI*. j\> x> yCL'~l. Similarly, Lt is the space of all finite sumsEl*. y]> xEL and y£L,_i. If Lr = 0 and Lr~19¿0, L is said to be solvable of index r. If L¡ = 0 and Lt-i^O, L is said to be nilpotent of length t. Definition. Let F be a subfield of R. A Lie algebra L over R

doi:10.2307/2034084
fatcat:mnz33vpotnelllob3uucku5dpu