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- W3098902948 abstract "The Killing form beta of a real (or complex) semisimple Lie group G is a left-invariant pseudo-Riemannian (or, respectively, holomorphic) Einstein metric. Let Omega denote the multiple of its curvature operator, acting on symmetric 2-tensors, with the factor chosen so that Omegabeta=2beta. The result of Meyberg [8], describing the spectrum of Omega in complex simple Lie groups G, easily implies that 1 is not an eigenvalue of Omega in any real or complex simple Lie group G except those locally isomorphic to SU(p,q), or SL(n,R), or SL(n,C) or, for even n only, SL(n/2,H), where pge qge0 and p+q=n>2. Due to the last conclusion, on simple Lie groups G other the ones just listed, nonzero multiples of the Killing form beta are isolated among left-invariant Einstein metrics. Meyberg's theorem also allows us to understand the kernel of Lambda, which is another natural operator. This in turn leads to a proof of a known, yet unpublished, fact: namely, that a semisimple real or complex Lie algebra with no simple ideals of dimension 3 is essentially determined by its Cartan three-form." @default.
- W3098902948 created "2020-11-23" @default.
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- W3098902948 date "2013-10-01" @default.
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- W3098902948 title "Curvature spectra of simple Lie groups" @default.
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- W3098902948 doi "https://doi.org/10.1007/s12188-013-0085-z" @default.
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