{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,15]],"date-time":"2026-05-15T16:44:01Z","timestamp":1778863441804,"version":"3.51.4"},"reference-count":25,"publisher":"World Scientific Pub Co Pte Ltd","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2009,5]]},"abstract":"<jats:p>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 \u2265 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].<\/jats:p>","DOI":"10.1142\/s0218196709005172","type":"journal-article","created":{"date-parts":[[2009,5,19]],"date-time":"2009-05-19T10:51:17Z","timestamp":1242730277000},"page":"347-371","source":"Crossref","is-referenced-by-count":6,"title":["UNIVERSAL ALGEBRA OF SECTORS"],"prefix":"10.1142","volume":"19","author":[{"given":"KATSUNORI","family":"KAWAMURA","sequence":"first","affiliation":[{"name":"College of Science and Engineering, Ritsumeikan University, 1-1-1 Noji Higashi, Kusatsu, Shiga 525-8577, Japan"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1007\/s002200200651"},{"key":"rf2","first-page":"043501-01","volume":"49","author":"Abe M.","journal-title":"J. Math. 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