Abstract
Cyclic metric Lie groups are Lie groups equipped with a left-invariant metric which is in some way far from being biinvariant, in a sense made explicit in terms of Tricerri and Vanhecke’s homogeneous structures. The semisimple and solvable cases are studied. We extend to the general case, Kowalski–Tricerri’s and Bieszk’s classifications of connected and simply-connected unimodular cyclic metric Lie groups for dimensions less than or equal to five.
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Communicated by A. Cap.
The first and third authors have been supported by the Ministry of Economy and Competitiveness, Spain, under Project MTM2011-22528. The second author has been supported by D.G.I. (Spain) and FEDER Projects MTM2010-15444 and MTM2013-46961-P. We are grateful to the referees for their interesting and useful reports, which have contributed to improve the presentation and, mainly, the contents of the paper. We acknowledge to one of the referees his/her comments on references [3, 12, 13], unknown to us, and their consequences.
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Gadea, P.M., González-Dávila, J.C. & Oubiña, J.A. Cyclic metric Lie groups. Monatsh Math 176, 219–239 (2015). https://doi.org/10.1007/s00605-014-0692-5
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DOI: https://doi.org/10.1007/s00605-014-0692-5