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The classification of 2-dimensional Jordan-ω-Lie algebras

Junxia Zhu

A complex Jordan-ω-Lie algebra is a vector space over the complex field, equipped with a symmetric bracket [−, −] and a bilinear form ω such that [[x, y], z] + [[y, z], x] + [[z, x], y] = ω(x, y)z + ω(y, z)x + ω(z, x)y for all x, y, z ∈ L. In this paper, we provide an approach to classify all 2-dimensional non-Jordan-Lie complex Jordan-ω-Lie algebras.