Locally conformal SKT almost abelian Lie algebras

A locally conformal SKT (shortly LCSKT) structure is a Hermitian structure (J,g) whose Bismut torsion 3-form H satisfies the condition dH=α∧H, for some closed non-zero 1-form α. This condition was introduced as a generalization of the SKT (or pluriclosed) condition dH=0. In this paper, we characterize the almost abelian Lie algebras admitting a Hermitian structure (J,g) such that dH=α∧H, for some closed 1-form α. As an application we classify LCSKT almost abelian Lie algebras in dimension 6. Finally, we also study on almost abelian Lie algebras the compatibility between the LCSKT condition and other types of Hermitian structures.