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Let g be a complex semisimple Lie algebra and U (g) be its enveloping algebra. We deduce from the work of R. Bezrukavnikov, A. Braverman and L. Positselskii that the Krull-Gabriel-Rentschler dimension of U (g) is equal to the dimension of a Borel subalgebra of g.doi:10.1090/s0002-9939-02-06507-3 fatcat:6a5qzm7j6jftzjgyqr7ugyqqqa