Abelian balanced Hermitian structures on unimodular Lie algebras

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 dime...

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Detalhes bibliográficos
Autores: Andrada, Adrián, Villacampa Gutierrez, Raquel
Formato: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2016
País:España
Recursos:Universidad de Zaragoza
Repositorio:Zaguán. Repositorio Digital de la Universidad de Zaragoza
OAI Identifier:oai:zaguan.unizar.es:61877
Acesso em linha:http://zaguan.unizar.es/record/61877
Access Level:acceso abierto
Descrição
Resumo: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.

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