Homology, Homotopy and Applications

Volume 7 (2005)

Number 1

Product structures on four dimensional solvable Lie algebras

Pages: 9 – 37

DOI: https://dx.doi.org/10.4310/HHA.2005.v7.n1.a2

Authors

A. Andrada (CIEM, FaMAF, Universidad Nacional de Córdoba, Ciudad Universitaria, Córdoba, Argentina)

M. L. Barberis (CIEM, FaMAF, Universidad Nacional de Córdoba, Ciudad Universitaria, Córdoba, Argentina)

I. G. Dotti (CIEM, FaMAF, Universidad Nacional de Córdoba, Ciudad Universitaria, Córdoba, Argentina)

G. P. Ovando (CIEM, FaMAF, Universidad Nacional de Córdoba, Ciudad Universitaria, Córdoba, Argentina)

Abstract

It is the aim of this work to study product structures on four dimensional solvable Lie algebras. We determine all possible paracomplex structures and consider the case when one of the subalgebras is an ideal. These results are applied to the case of Manin triples and complex product structures. We also analyze the three dimensional subalgebras.

Keywords

solvable Lie algebra, product structure, paracomplex structure

2010 Mathematics Subject Classification

Primary 53C15. Secondary 22E25.

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Published 1 January 2005