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We study the Lorentz and CPT violating effects on the branching ratio BR, theCPT violating asymmetry A_{CPT} and the ratio of the decay width, includingonly the Lorentz violating effects, to the one obtained in the standard model,for the flavor dependent part of the lepton flavor conserving Z\to l^+ l^-(l=e,\mu,\tau) decay. The inclusion of the Lorentz and CPT violating effects tothe standard model contribution is too small to be detected, since thecorresponding coefficients are highly suppressed at the low energy scale.Comment: 11 pages, 6 figure

The Lorentz and CPT violating effects on the $Z\rightarrow l^ + l^-$ decay