Representations of the comtrans algebra of n × n matrices

Abstract

We show that the universal enveloping algebra of the comtrans algebra of all n × n (n > 2) matrices over a field of characteristic 0 with respect to the trilinear operations: (the special commutator) and (the special translator) is finite-dimensional. We explicitly determine the decomposition of the universal envelope into matrix algebras. We also show that the universal enveloping algebra of a comtrans algebra is not necessary be finite-dimensional.