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 dimen...
| Authors: | , |
|---|---|
| Format: | article |
| Status: | Published version |
| Publication Date: | 2016 |
| Country: | Argentina |
| Institution: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repository: | CONICET Digital (CONICET) |
| Language: | English |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/59788 |
| Online Access: | http://hdl.handle.net/11336/59788 |
| Access Level: | Open access |
| Keyword: | BISMUT CONNECTION BALANCED HERMITIAN METRIC ABELIAN COMPLEX STRUCTURE https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Summary: | 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. |
|---|