ABELIAN BALANCED HERMITIAN STRUCTURES ON UNIMODULAR LIE ALGEBRAS |
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Authors: | ADRIÁN ANDRADA RAQUEL VILLACAMPA |
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Institution: | 1.FaMAF-CIEM,Universidad Nacional de Córdoba,Córdoba,Argentina;2.Centro Universitario de la Defensa, Zaragoza-I.U.M.A.,Academia General Militar,Zaragoza,Spain |
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Abstract: | 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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