doi:10.1007/S00031-015-9352-7engAndrada, AdriánVillacampa Gutierrez, RaquelAbelian balanced Hermitian structures on unimodular Lie algebrasART-2016-99255Let 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.2016http://zaguan.unizar.es/record/6187710.1007/S00031-015-9352-7http://zaguan.unizar.es/record/61877oai:zaguan.unizar.es:61877info:eu-repo/grantAgreement/ES/DGA/E15info:eu-repo/grantAgreement/ES/MICINN/MTM2011-28326-C02-01TRANSFORMATION GROUPS 21, 4 (2016), 903-927All rights reservedhttp://www.europeana.eu/rights/rr-f/info:eu-repo/semantics/openAccess