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Leibniz algebras associated with some finite-dimensional representation of Diamond Lie algebra

Leibniz algebras associated with some finite-dimensional representation of Diamond Lie algebra

In this paper we classify Leibniz algebras whose associated Lie algebra is four-dimensional Diamond Lie algebra and the ideal generated by squares of elements is represented by one of the finite-dimensional indecomposable D-modules Un 1, Un 2 or Wn 1 or Wn 2.