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  Are there any relation between Einstein structure on a Lie group and chirality of its Lie algebra?

+ 1 like - 0 dislike

An Einstein structure is a  Riemannian metric on a manifold M such that $Ric=k g$   for  a  constant  $k$. $Ric$ is the Ricci tensor and $g$ is the metric tensor


Are  there  any relations between existence of  an  Einstein structure on a Lie  group  and  chirality of its  Lie  algebra? Under  what  conditions  a Lie  group whose  Lie  algebra is  a  chiral algebra admit an Einstein structure?

asked Jun 20, 2023 in Theoretical Physics by AliTaghavi(Math) (140 points) [ revision history ]
recategorized Jul 5, 2023 by Dilaton

What is an Einstein structure? Please give a reference.

@ArnoldNeumaier   Thank you for your comment. An Einstein structure is a  Riemannian metric on a manifold M such that Ric=k g   for  a  constant  k. Ric is the Ricci tensor and g is the metric tensor


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