Construction of the Invariants of the Simple Lie Groups

  • L. O’Raifeartaigh


To introduce the problem which I should like to consider in this talk, let me first make some remarks about the three-dimensional rotation group O3, with which we are familiar. For this group, the infinitesimal generators Ti, i = 1, 2, 3, satisfy the commutation relations
$${\text{[}}{T_i}{T_j}{\text{] = }}i{T_k}{\text{ (}}i,j,k{\text{ cyclic)}}$$
and there exists a polynomial in the Ti, namely,
$$\mathop T\nolimits^2 = \;\mathop T\nolimits_1^2 + \mathop T\nolimits_2^2 + \mathop T\nolimits_3^2$$
which has the property that it commutes with all of the infinitesimal generators:
$$[{T^2},{T_i}]\; = \;0\;\;(i = 1,2,3)$$


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Copyright information

© Plenum Press 1966

Authors and Affiliations

  • L. O’Raifeartaigh
    • 1
  1. 1.Dublin Institute for Advanced StudiesDublinIreland

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