Celebratio Mathematica — Jones

Complete Bibliography

Works connected to David Penneys

Filter the Bibliography List

year	title	people

			clear

V. F. R. Jones and D. Penneys: “The embedding theorem for finite depth subfactor planar algebras,” Quantum Topol. 2 : 3 (2011), pp. 301–337. MR 2812459 Zbl 1230.46055 ArXiv 1007.3173 article

V. F. R. Jones and D. Penneys: “Infinite index subfactors and the GICAR categories,” Comm. Math. Phys. 339 : 2 (2015), pp. 729–768. MR 3370617 Zbl 1338.46067 ArXiv 1410.0856 article

Given a \( \mathrm{II}_1 \)-subfactor \( A\subset B \) of arbitrary index, we show that the rectangular GICAR category, also called the rectangular planar rook category, faithfully embeds as \( A - A \) bimodule maps among the bimodules \( \bigotimes_A^n L^2(B) \). As a corollary, we get a lower bound on the dimension of the centralizer algebras \( A^{\prime}_0\cap A_{2n} \) for infinite index subfactors, and we also get that \( A^{\prime}_0\cap A_{2n} \) is nonabelian for \( n\geq 2 \), where \( (A_n)_{n\geq 0} \) is the Jones tower for \( A_0 = A \subset B = A_1 \). We also show that the annular GICAR/planar rook category acts as maps amongst the \( A \)-central vectors in \( \bigotimes_A^n L^2(B) \), although this action may be degenerate. We prove these results in more generality using bimodules. The embedding of the GICAR category builds on work of Connes and Evans, who originally found GICAR algebras inside Temperley–Lieb algebras with finite modulus.

The 2014 Maui and 2015 Qinhuangdao conferences in honour of Vaughan F. R. Jones’ 60th birthday (Kihei, HI, 14–18 July 2014 and Qinhuangdao, China 13–17 July 2015). Edited by S. Morrison and D. Penneys. Proceedings of the Centre for Mathematics and its Applications 46. Australian National University (Canberra), 2017. MR 3635666 Zbl 1386.46002 book

Scott Morrison	Related
David Penneys	Related