Abstract
We show that a nontrivial example of universal algebra appears in quantum field theory. For a unital C *-algebra [Formula: see text], a sector is a unitary equivalence class of unital *-endomorphisms of [Formula: see text]. We show that the set [Formula: see text] of all sectors of [Formula: see text] is a universal algebra with an N-ary sum which is not reduced to any binary sum when [Formula: see text] includes the Cuntz algebra [Formula: see text] as a C *-subalgebra with common unit for N ≥ 3. Next we explain that the set [Formula: see text] of all unitary equivalence classes of unital *-representations of [Formula: see text] is a right module of [Formula: see text]. An essential algebraic formulation of branching laws of representations is given by using submodules of [Formula: see text]. As an application, we show that the action of [Formula: see text] on [Formula: see text] distinguishes elements of [Formula: see text].
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