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An angular analysis of Lambda_b0 -> J/psi Lambda decays is performed using a data sample corresponding to 1.0 fb^{-1} collected in pp collisions at sqrt(s) = 7 TeV with the LHCb detector at the LHC. A parity violating asymmetry parameter characterising the Lambda_b0 -> J/psi Lambda decay of 0.05 +/- 0.17 +/- 0.07 and a Lambda_b0 transverse production polarisation of 0.06 +/- 0.07 +/- 0.02 are measured, where the first uncertainty is statistical and the second systematic.

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