Abelian balanced Hermitian structures on unimodular Lie algebras

ADRIÁN ANDRADA; RAQUEL VILLACAMPA

TRANSFORMATION GROUPS

BIRKHAUSER BOSTON INC

Año: 2016 vol. 21 p. 903 - 927

1083-4362

Let g be a 2n-dimensional unimodular Lie algebra equipped with a Hermitian structure (J,F) such that the complex structure J is abelian and the fundamental form F is balanced.  We prove that the holonomy group of the associated Bismut connection reduces to a subgroup of SU(n-k), being 2k the dimension of the center of g. We determine conditions that allow a unimodular Lie algebra to admit this particular type of structures. Moreover, we give methods to construct them in arbitrary dimensions and classify them if the Lie algebra is 8-dimensional and nilpotent.