Abstract
Starting from a Kemmer algebra generated by n elements, a new algebra generated by ½(n2 + n) elements is derived. This algebra has only one irreducible representation which is of dimension (n + 1). This representation is equivalent to the first elementary representation of the infinitesimal operators of the unitary group in a space of (n + 1) dimensions. Omitting the identity element, one of course obtains the first elementary representation of the unitary unimodular group in a space of (n + 1) dimensions. The procedure is first illustrated for the case of n = 3 and explicit representations of the infinitesimal operators of U4 (SU4) are obtained. Next, the proof for arbitrary n is outlined. Finally, the degenerate case of U3 (SU3) is discussed.
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