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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 . Fundamental results about finite-dimensional -Lie algebras were developed by Zusmanovich . In , 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 .
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Yin Chen, Chang Liu, Runxuan Zhang, Classification of three-dimensional complex -Lie algebras. Port. Math. 71 (2014), no. 2, pp. 97–108DOI 10.4171/PM/1943