Braided Endomorphisms of Cuntz Algebras
AbstractWe 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.
How to Cite
Conti, R., & Fidaleo, F. (2000). Braided Endomorphisms of Cuntz Algebras. MATHEMATICA SCANDINAVICA, 87(1), 93–114. https://doi.org/10.7146/math.scand.a-14301