Classification of three-dimensional complex -Lie algebras

  • Yin Chen

    Northeast Normal University, Changchun, China
  • Chang Liu

    Northeast Normal University, Changchun, China
  • Runxuan Zhang

    Northeast Normal University, Changchun, China

Abstract

A complex -Lie algebra is a vector space over the complex field, equipped with a skew-symmetric bracket and a bilinear form such that

for all . The notion of -Lie algebras, as a generalization of Lie algebras, was introduced in Nurowski [3]. Fundamental results about finite-dimensional -Lie algebras were developed by Zusmanovich [5]. In [3], all three-dimensional non-Lie real -Lie algebras were classified. The purpose of this note is to provide an approach to classify all three-dimensional non-Lie complex -Lie algebras. Our method also gives a new proof of the classification in Nurowski [3].

Cite this article

Yin Chen, Chang Liu, Runxuan Zhang, Classification of three-dimensional complex -Lie algebras. Port. Math. 71 (2014), no. 2, pp. 97–108

DOI 10.4171/PM/1943