Algebra of sectors
نویسنده
چکیده
The set SectA of all unitary equivalence classes of unital ∗-endomorphisms of a unital C∗-algebra A is called the sector of A. We show that there is an exotic algebraic structure on SectA when A includes a Cuntz algebra as a C∗-subalgebra with common unit. Next we explain that the set BSpecA of all unitary equivalence classes of unital ∗-representations of A is a right module of SectA. An essential algebraic formulation of branching laws of representations is given by submodules of BSpecA. As application, we show that the action of SectA on BSpecA distinguishes elements of SectA.
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