Abstract
In this paper we construct a minimal faithful representation of the (2 m+ 2) -dimensional complex general Diamond Lie algebra, Dm(C) , which is isomorphic to a subalgebra of the special linear Lie algebra sl(m+ 2 , C). We also construct a faithful representation of the real general Diamond Lie algebra Dm which is isomorphic to a subalgebra of the special symplectic Lie algebra sp(2 m+ 2 , R). Furthermore, we describe Leibniz algebras with corresponding (2 m+ 2) -dimensional real general Diamond Lie algebra Dm and such that the ideal generated by the squares of elements provides a faithful representation of Dm.
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