Nilpotent Lie algebras with 2-dimensional commutator ideals

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7 Citations (Scopus)

Abstract

We classify all (finitely dimensional nilpotent Lie k-algebras h with 2-dimensional commutator ideals h', extending a known result to the case where h' is non-central and k is an arbitrary field. It turnsout that, while the structure of h depends on the field k if h' is central, it is independent of k if h' is non-central and is uniquely determined by the dimension of h. In the case where k is algebraically or real closed, we also list all nilpotent Lie k-algebras h with 2-dimensional central commutator ideals h' and dimk h < 12.
Original languageEnglish
Pages (from-to)650-656
Number of pages7
JournalLinear Algebra and Its Applications
Volume434
Publication statusPublished - 2011

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

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