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articleNo Access
UNIVERSAL ALGEBRA OF SECTORS
- KATSUNORI KAWAMURA
International Journal of Algebra and Computation01 May 2009
Preview Abstract
We show that a nontrivial example of universal algebra appears in quantum field theory. For a unital C*-algebra , a sector is a unitary equivalence class of unital *-endomorphisms of . We show that the set of all sectors of is a universal algebra with an N-ary sum which is not reduced to any binary sum when includes the Cuntz algebra as a C*-subalgebra with common unit for N ≥ 3. Next we explain that the set of all unitary equivalence classes of unital *-representations of is a right module of . An essential algebraic formulation of branching laws of representations is given by using submodules of . As an application, we show that the action of on distinguishes elements of .

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