Balanced Hermitian structures on twisted cartesian products

Abstract

We study Hermitian structures on twisted cartesian products $(\mathfrak{g}_{(ρ_{1},ρ_{2})},\mathrm{J},\cal{K})$ of two Hermitian Lie algebras according to two representations $ρ_{1}$ and $ρ_{2}$. We give the conditions on $(\mathfrak{g}_{(ρ_{1},ρ_{2})},\mathrm{J},\cal{K})$ to be balanced and locally conformally balanced. As an application we classify six-dimensional balanced Hermitian twisted cartesian products Lie algebras.