We discuss sufficient conditions ensuring that certain endomorphisms of infinite factors arising from Cuntz algebras are braided. We analyse some explicit non-trivial examples associated to unitary solutions of quantum Yang-Baxter equations on a Hilbert space of dimension 2. In particular we show the existence of endomorphisms of index 2 associated to representations of Hecke algebras at a primitive fourth root of unity. In this case we compute the associated fusion rules. These fusion rules define a finitely generated *-semiring which is not finite. Such a picture seems to be closely related to the description of (the dual of) a deformation, at a fourth root of unity, of some compact matrix group. This could be of some interest for the investigation of quantum summetries naturally appearing in low-dimensional Quantum Field Theory.

Conti, R., & Fidaleo, F. (2000). Braided endomorphisms of Cuntz algebras. MATHEMATICA SCANDINAVICA, 87(1) [10.7146/math.scand.a-14301].

Braided endomorphisms of Cuntz algebras

FIDALEO Francesco
2000

Abstract

We discuss sufficient conditions ensuring that certain endomorphisms of infinite factors arising from Cuntz algebras are braided. We analyse some explicit non-trivial examples associated to unitary solutions of quantum Yang-Baxter equations on a Hilbert space of dimension 2. In particular we show the existence of endomorphisms of index 2 associated to representations of Hecke algebras at a primitive fourth root of unity. In this case we compute the associated fusion rules. These fusion rules define a finitely generated *-semiring which is not finite. Such a picture seems to be closely related to the description of (the dual of) a deformation, at a fourth root of unity, of some compact matrix group. This could be of some interest for the investigation of quantum summetries naturally appearing in low-dimensional Quantum Field Theory.
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/05 - Analisi Matematica
eng
Conti, R., & Fidaleo, F. (2000). Braided endomorphisms of Cuntz algebras. MATHEMATICA SCANDINAVICA, 87(1) [10.7146/math.scand.a-14301].
Conti, R; Fidaleo, F
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2108/205877
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