Simplicity of the quasilocal algebra of the system of canonical anticommutation relations with compact gauge group

A study is made of a system of canonical anticommutation relations whose physical observables are distinguished by gauge invariance under an arbitrary compact gauge group. It is shown that the $C^*$-algebra of quasilocal observables of such a system is simple. In contrast to the usual methods of investigating canonical anticommutalion relations, the proof is based on the properties of local algebras.