We survey a recent progress on algebraic quantum field theory in connection with subfactor theory. We mainly concentrate on one-dimensional conformal quantum field theory.
Let M be a typeⅡ1 factor,G be a finite group,and N■M be an irreducible subfactor of finite index.We prove that the composed lattice of the intermediate subfactor lattice for the inclusion N■M and the subgroup latti...Let M be a typeⅡ1 factor,G be a finite group,and N■M be an irreducible subfactor of finite index.We prove that the composed lattice of the intermediate subfactor lattice for the inclusion N■M and the subgroup lattice of G can be realized as an intermediate subfactor lattice of a certain composed subfactor of finite index,and this subfactor also has finite depth when N■M has finite depth.展开更多
We introduce block maps for subfactors and study their dynamic systems. We prove that the limit points of the dynamic system are positive multiples of biprojections and zero. For the Z2 case, the asymptotic phenomenon...We introduce block maps for subfactors and study their dynamic systems. We prove that the limit points of the dynamic system are positive multiples of biprojections and zero. For the Z2 case, the asymptotic phenomenon of the block map coincides with that of the 2 D Ising model. The study of block maps requires a further development of our recent work on the Fourier analysis of subfactors. We generalize the notion of sum set estimates in additive combinatorics for subfactors and prove the exact inverse sum set theorem. Using this new method, we characterize the extremal pairs of Young’s inequality for subfactors, as well as the extremal operators of the Hausdorff-Young inequality.展开更多
In this paper,we calculate the norm of the string Fourier transform on subfactor planar algebras and characterize the extremizers of the inequalities for parameters 0<p,q≤∞.Furthermore,we establish Renyi entropic...In this paper,we calculate the norm of the string Fourier transform on subfactor planar algebras and characterize the extremizers of the inequalities for parameters 0<p,q≤∞.Furthermore,we establish Renyi entropic uncertainty principles for subfactor planar algebras.展开更多
Ge(2003)asked the question whether LF∞can be embedded into LF2 as a maximal subfactor.We answer it affirmatively with three different approaches,all containing the same key ingredient:the existence of maximal subgrou...Ge(2003)asked the question whether LF∞can be embedded into LF2 as a maximal subfactor.We answer it affirmatively with three different approaches,all containing the same key ingredient:the existence of maximal subgroups with infinite index.We also show that point stabilizer subgroups for every faithful,4-transitive action on an infinite set give rise to maximal von Neumann subalgebras.By combining this with the known results on constructing faithful,highly transitive actions,we get many maximal von Neumann subalgebras arising from maximal subgroups with infinite index.展开更多
文摘We survey a recent progress on algebraic quantum field theory in connection with subfactor theory. We mainly concentrate on one-dimensional conformal quantum field theory.
基金supported by National Natural Science Foundation of China(Grant No.11871130)the Fundamental Research Funds for the Central Universities of China(Grant No.DUT18LK23)supported by National Natural Science Foundation of China(Grant No.11871150)。
文摘Let M be a typeⅡ1 factor,G be a finite group,and N■M be an irreducible subfactor of finite index.We prove that the composed lattice of the intermediate subfactor lattice for the inclusion N■M and the subgroup lattice of G can be realized as an intermediate subfactor lattice of a certain composed subfactor of finite index,and this subfactor also has finite depth when N■M has finite depth.
基金supported by National Natural Science Foundation of China (Grant No. A010602)National Excellent Doctoral Dissertation of China (Grant No. 201116)+2 种基金supported by the Templeton Religion Trust (Grant Nos. TRT0080 and TRT0159)an AMS-Simons Travel Grantsupported by National Natural Science Foundation of China (Grant Nos. 11771413 and 11401554)
文摘We introduce block maps for subfactors and study their dynamic systems. We prove that the limit points of the dynamic system are positive multiples of biprojections and zero. For the Z2 case, the asymptotic phenomenon of the block map coincides with that of the 2 D Ising model. The study of block maps requires a further development of our recent work on the Fourier analysis of subfactors. We generalize the notion of sum set estimates in additive combinatorics for subfactors and prove the exact inverse sum set theorem. Using this new method, we characterize the extremal pairs of Young’s inequality for subfactors, as well as the extremal operators of the Hausdorff-Young inequality.
基金supported by Templeton Religion Trust(Grant No.TRT0159)supported by National Natural Science Foundation of China(Grant No.11771413)Templeton Religion Trust(Grant No.TRT0159)。
文摘In this paper,we calculate the norm of the string Fourier transform on subfactor planar algebras and characterize the extremizers of the inequalities for parameters 0<p,q≤∞.Furthermore,we establish Renyi entropic uncertainty principles for subfactor planar algebras.
基金the National Science Center(NCN)(Grant No.2014/14/E/ST1/00525)Institute of Mathematics,Polish Academy of Sciences(IMPAN)from the Simons Foundation(Grant No.346300)the Matching 2015-2019 Polish Ministry of Science and Higher Education(MNiSW)Fund,and the Research Foundation-Flanders-Polish Academy of Sciences(FWO-PAN).
文摘Ge(2003)asked the question whether LF∞can be embedded into LF2 as a maximal subfactor.We answer it affirmatively with three different approaches,all containing the same key ingredient:the existence of maximal subgroups with infinite index.We also show that point stabilizer subgroups for every faithful,4-transitive action on an infinite set give rise to maximal von Neumann subalgebras.By combining this with the known results on constructing faithful,highly transitive actions,we get many maximal von Neumann subalgebras arising from maximal subgroups with infinite index.
