ترغب بنشر مسار تعليمي؟ اضغط هنا

Fusion symmetric spaces and subfactors

114   0   0.0 ( 0 )
 نشر من قبل Hans Wenzl
 تاريخ النشر 2011
  مجال البحث
والبحث باللغة English
 تأليف Hans Wenzl




اسأل ChatGPT حول البحث

We construct analogs of the embedding of orthogonal and symplectic groups into unitary groups in the context of fusion categories. At least some of the resulting module categories also appear in boundary conformal field theory. We determine when these categories are unitarizable, and explicitly calculate the index and principal graph of the resulting subfactors.



قيم البحث

اقرأ أيضاً

195 - Marta Asaeda 2007
We show that any graph, in the sequence given by Haagerup in 1991 as that of candidates of principal graphs of subfactors, is not realized as a principal graph except for the smallest two. This settles the remaining case of a previous work of the first author.
To a proper inclusion Nsubset M of II_1 factors of finite Jones index [M:N], we associate an ergodic C*-action of the quantum group S_mu U(2). The deformation parameter is determined by -1<mu<0 and [M:N]=|mu+mu^{-1}|. The higher relative commutants c an be identified with the spectral spaces of the tensor powers of the defining representation of the quantum group. This ergodic action may be thought of as a virtual subgroup of S_mu U(2) in the sense of Mackey arising from the tensor category generated by M regarded as a bimodule over N. mu is negative as M is a real bimodule.
109 - Michael Burns 2011
Growing out of the initial connections between subfactors and knot theory that gave rise to the Jones polynomial, Jones axiomatization of the standard invariant of an extremal finite index $II_1$ subfactor as a spherical $C^*$-planar algebra, present ed in arXiv:math.QA/9909027, is the most elegant and powerful description available. We make the natural extension of this axiomatization to the case of finite index subfactors of arbitrary type. We also provide the first steps toward a limited planar structure in the infinite index case. The central role of rotations, which provide the main non-trivial part of the planar structure, is a recurring theme throughout this work. In the finite index case the axioms of a $C^*$-planar algebra need to be weakened to disallow rotation of internal discs, giving rise to the notion of a rigid $C^*$-planar algebra. We show that the standard invariant of any finite index subfactor has a rigid $C^*$-planar algebra structure. We then show that rotations can be re-introduced with associated correction terms entirely controlled by the Radon-Nikodym derivative of the two canonical states on the first relative commutant, $N cap M$. By deforming a rigid $C^*$-planar algebra to obtain a spherical $C^*$-planar algebra and lifting the inverse construction to the subfactor level we show that any rigid $C^*$-planar algebra arises as the standard invariant of a finite index $II_1$ subfactor equipped with a conditional expectation, which in general is not trace preserving. Jones results thus extend completely to the general finite index case. We conclude by applying our machinery to the $II_1$ case, shedding new light on the rotations studied by Huang [11] and touching briefly on the work of Popa [29]. (continued in article)
62 - K.-H. Rehren 1999
Canonical tensor product subfactors (CTPSs) describe, among other things, the embedding of chiral observables in two-dimensional conformal quantum field theories. A new class of CTPSs is constructed some of which are associated with certain modular i nvariants, thereby establishing the expected existence of the corresponding two-dimensional theories.
Let $mathcal{M}$ be an atomless semifinite von Neumann algebra (or an atomic von Neumann algebra with all atoms having the same trace) acting on a (not necessarily separable) Hilbert space $H$ equipped with a semifinite faithful normal trace $tau$. L et $E(mathcal{M},tau) $ be a symmetric operator space affiliated with $ mathcal{M} $, whose norm is order continuous and is not proportional to the Hilbertian norm $left|cdotright|_2$ on $L_2(mathcal{M},tau)$. We obtain general description of all bounded hermitian operators on $E(mathcal{M},tau)$. This is the first time that the description of hermitian operators on asymmetric operator space (even for a noncommutative $L_p$-space) is obtained in the setting of general (non-hyperfinite) von Neumann algebras. As an application, we resolve a long-standing open problem concerning the description of isometries raised in the 1980s, which generalizes and unifies numerous earlier results.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا