RESEARCH ARTICLE

Uncountably many non-isomorphic nilpotent real $n$-Lie algebras

Ernest Stitzinger, Michael P. Williams

North Carolina State University, Box 8205, Raleigh, NC 27695

Abstract: There are an uncountable number of non-isomorphic nilpotent real Lie algebras for every dimension greater than or equal to 7. We extend an old technique, which applies to Lie algebras of dimension greater than or equal to 10, to find corresponding results for $n$-Lie algebras. In particular, for $n\ge 6$, there are an uncountable number of non-isomorphic nilpotent real $n$-Lie algebras of dimension $n+4$.

Keywords: $n$-Lie algebras, nilpotent, algebraically independent, transcendence degree.

MSC: 17A42

Language: English

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