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Realizing the braided Temperley-Lieb-Jones C*-tensor categories as Hilbert C*-modules | | Andreas Næs Aaserud
; David E. Evans
; | | Date: |
7 Aug 2019 | | Abstract: | We associate to each Temperley-Lieb-Jones C*-tensor category
$mathcal{T}!mathcal{L}mathcal{J}(delta)$ with parameter $delta$ in the
discrete range ${2cos(pi/(k+2)),:,k=1,2,ldots}cup{2}$ a certain
C*-algebra $mathcal{B}$ of compact operators. We use the unitary braiding on
$mathcal{T}!mathcal{L}mathcal{J}(delta)$ to equip the category
$mathrm{Mod}_{mathcal{B}}$ of (right) Hilbert $mathcal{B}$-modules with the
structure of a braided C*-tensor category. We show that
$mathcal{T}!mathcal{L}mathcal{J}(delta)$ is equivalent, as a braided
C*-tensor category, to the full subcategory $mathrm{Mod}_{mathcal{B}}^f$ of
$mathrm{Mod}_{mathcal{B}}$ whose objects are those modules which admit a
finite orthonormal basis. Finally, we indicate how these considerations
generalize to arbitrary finitely generated rigid braided C*-tensor categories. | | Source: | arXiv, 1908.2674 | | Services: | Forum | Review | PDF | Favorites | |
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