Abstract
Until a couple of years ago, the only known examples of Lie groups admitting left-invariant metrics with negative Ricci curvature were either solvable or semisimple.We use a general construction from a previous article of the second named author to produce a large number of examples with compact Levi factor. Given a compact semisimple real Lie algebra 𝔲 and a real representation π satisfying some technical properties, the construction returns a metric Lie algebra (𝔲, π) with negative Ricci operator. In this paper, when u is assumed to be simple, we prove that 𝔩(𝔲, π) admits a metric having negative Ricci curvature for all but finitely many finite-dimensional irreducible representations of 𝔲⨂ℝℂ, regarded as a real representation of 𝔲. We also prove in the last section a more general result where the nilradical is not abelian, as it is in every (𝔲, π).
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EMILIO A. LAURET is Supported by CONICET, FONCYT, and the Alexander von Humboldt Foundation (return fellowship).
CYNTHIA E. WILL is Supported by CONICET, FONCYT, and SeCyT (Universidad Nacional de CĂłrdoba).
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LAURET, E.A., WILL, C.E. NON-SOLVABLE LIE GROUPS WITH NEGATIVE RICCI CURVATURE. Transformation Groups 27, 163–179 (2022). https://doi.org/10.1007/s00031-020-09582-4
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DOI: https://doi.org/10.1007/s00031-020-09582-4