Abstract
It is the aim of this work to give a characterization of the two-step nilpotent Lie algebras carrying abelian hypercomplex structures. In the special case of trivial extensions of irreducible H-type Lie algebras this characterization is given in terms of the dimension of the commutator subalgebra. As a consequence, we obtain the corresponding theorem for arbitrary H-type Lie algebras, extending a result in Barberis and Dotti, J. Math. Oxford (2) 47 (1996) 389–404.
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