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Recent work on the Bondi-Metzner-Sachs group introduced a class of functions sYlm(θ, φ) defined on the sphere and a related differential operator ð. In this paper the sYlm are related to the representation matrices of the rotation group R3 and the properties of ð are derived from its relationship to an angular-momentum raising operator. The relationship of the sTlm(θ, φ) to the spherical harmonics of R4 is also indicated. Finally using the relationship of the Lorentz group to the conformal group of the sphere, the behavior of the sTlm under this latter group is shown to realize a representation of the Lorentz group.

The forms of the invariant primitive tensors for the simple Lie algebras A_l, B_l, C_l and D_l are investigated. A new family of symmetric invariant tensors is introduced using the non-trivial cocycles for the Lie algebra cohomology. For the A_l algebra it is explicitly shown that the generic forms of these tensors become zero except for the l primitive ones and that they give rise to the l primitive Casimir operators. Some recurrence and duality relations are given for the Lie algebra cocycles. Tables for the 3- and 5-cocycles for su(3) and su(4) are also provided. Finally, new relations involving the d and f su(n) tensors are given.Comment: Latex file. 34 pages. (Trivial) misprints corrected. To appear in Nucl. Phys.

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Summary Intravenous lidocaine is used widely for its effect on postoperative pain and recovery but it can be, and has been, fatal when used inappropriately and incorrectly. The risk‐benefit ratio of i.v. lidocaine varies with type of surgery and with patient factors such as comorbidity (including pre‐existing chronic pain). This consensus statement aims to address three questions. First, does i.v. lidocaine effectively reduce postoperative pain and facilitate recovery? Second, is i.v. lidocaine safe? Third, does the fact that i.v. lidocaine is not licensed for this indication affect its use? We suggest that i.v. lidocaine should be regarded as a ‘high‐risk’ medicine. Individual anaesthetists may feel that, in selected patients, i.v. lidocaine may be beneficial as part of a multimodal peri‐operative pain management strategy. This approach should be approved by hospital medication governance systems, and the individual clinical decision should be made with properly informed consent from the patient concerned. If i.v. lidocaine is used, we recommend an initial dose of no more than 1.5 mg.kg‐1, calculated using the patient’s ideal body weight and given as an infusion over 10 min. Thereafter, an infusion of no more than 1.5 mg.kg‐1.h‐1 for no longer than 24 h is recommended, subject to review and re‐assessment. Intravenous lidocaine should not be used at the same time as, or within the period of action of, other local anaesthetic interventions. This includes not starting i.v. lidocaine within 4 h after any nerve block, and not performing any nerve block until 4 h after discontinuing an i.v. lidocaine infusion.