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Haagerup subfactor

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August undefined, 2024

WebMar 1, 2012 · In addition to the two even parts of the Haagerup subfactor, there is exactly one more fusion category which is Morita equivalent to each of them. This third fusion category has six simple objects and the same fusion rules as one of the even parts of the Haagerup subfactor, but has not previously appeared in the literature. http://web.math.ku.dk/~haagerup/index.php?show=all

Uffe Haagerup

WebJan 29, 2015 · The first subfactor above index 4, the Haagerup subfactor, is increasingly well understood and appears to lie in a (discrete) infinite family of subfactors where the … Uffe Haagerup's mathematical focus has been on the fields of operator algebra, group theory and geometry, but his publications has a broad scope and also involves free probability theory and random matrices. He has participated in many international mathematical groups and networks from early on, and has worked as ordinary contributor and participator, organizer, lecturer and editor. claus vandborg

Uffe Haagerup - Wikipedia

WebSep 26, 2012 · We construct a new subfactor planar algebra, and as a corollary a new subfactor, with the ‘extended Haagerup’ principal graph pair. This completes the … WebApr 15, 2014 · In this paper we construct two new fusion categories and many new subfactors related to the exceptional Extended Haagerup subfactor. The Extended … WebHaagerup’s original result did not specify which of the possible principal graphs are actually realized. Considerable progress has since been made in this direction. Asaeda and Haagerup [2] proved the existence and uniqueness of a subfactor pla-nar algebra whose principal graphs are H0 (called the Haagerup subfactor), and claus von bulow girlfriend

[PDF] The Asaeda–Haagerup fusion categories Semantic Scholar

A PLANAR ALGEBRA CONSTRUCTION OF THE HAAGERUP …

WebOct 24, 2024 · This classification was initiated by Uffe Haagerup. It uses (among other things) a listing of possible principal graphs, together with the embedding theorem and the jellyfish algorithm. A subfactor planar algebra remembers the subfactor (i.e. its standard invariant is complete) if it is amenable. WebJan 11, 2024 · The simplest example that requires new techniques for building a CFT is the Haagerup subfactor, since it is the smallest subfactor with index larger than 4. In this thesis, we investigate the question whether there is a CFT corresponding to the Haagerup subfactor via lattice models in one and two dimensions. The first task here is to find the … claus werningerWebJan 25, 2012 · The Haagerup subfactor is the smallest index finite depth subfactor which does not occur in one of these families. In this paper we construct the planar algebra … download surface laptop 4 firmware

"WebOct 14, 2024 · The Extended Haagerup subfactor has two even parts EH1 and EH2. These fusion categories are mysterious and are the only known fusion categories which appear to be unrelated to finite groups, quantum groups, or Izumi quadratic categories. One key technique which has previously revealed hidden structure in fusion categories is to study … " - Haagerup subfactor

Haagerup subfactor

Conferences – Center for Noncommutative Geometry and …

Webdepth 6, with one exception, the principal graph of the Haagerup subfactor. A II 1 subfactor is an inclusion AˆBof in nite von Neumann algebras with trivial centre and a compatible trace with tr(1) = 1. In this setting, one can analyze the bimodules generated by AB B and BB A. The principal graph of a subfactor has as vertices the WebJun 7, 2010 · The quantum double of the Haagerup subfactor, the first irreducible finite depth subfactor with index above 4, is the most obvious candidate for exotic modular data. We show that its modular data...

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WebJan 10, 2014 · I’ll tell you about some of the most exciting examples, including the Temperley-Lieb algebra (and its relation to knot theory), the color-counting planar algebra (and the five-color theorem), and the extended Haagerup subfactor (joint work with Bigelow, Morrison and Snyder). WebFeb 1, 2010 · Etingof, Nikshych and Ostrik ask in arXiv:math.QA/0203060 if every fusion category can be completely defined over a cyclotomic field. We show that this is not the case: in particular one of the fusion categories coming from the Haagerup subfactor arXiv:math.OA/9803044 and one coming from the newly constructed extended …

WebIn mathematics, the Haagerup property, named after Uffe Haagerup and also known as Gromov's a-T-menability, is a property of groups that is a strong negation of Kazhdan's … WebU. Haagerup and E. Størmer, Subfactors of a factor of type III-lambda, which contain a maximal centralizer, International Journal Math. 6, 273-277 (1995). U. Haagerup and T. Itoh, Grothendieck type inequalities for bilinear forms on C*-algebras, J. Operator theory 34, 263-283 (1995).

Webfactor, now called the Haagerup subfactor (see [2] for the proof). The Haagerup subfactor is the ﬁrst subfactor that is not directly related to either an ordinary group or a quantum group, and whether its Drinfeld center is related to a quantum group (conformal ﬁeld theory) or not is an interesting open problem. At the time of writ- WebTo construct the extended Haagerup subfactor, we start with the graph planar algebra of its principal graph eH. GPA(eH) 8;+ is 148475-dimensional; luckily the subspace X of uncappable, ˆ= 1 elements of GPA(eH) 8;+ is only 19-dimensional. Unluckily, it is not natural in our given basis. We nd an element S 2X which further satis es S S 8 8 8 = f ...

Web2.20 The Haagerup subfactor The Haagerup subfactor [AH99] is a ﬁnite-depth subfactor with index 5+ √ 13 2; this is the smallest index above 4 for any ﬁnite depth …

WebMay 29, 2013 · The Haagerup property, which is a strong converse of Kazhdan's property $(T)$, has translations and applications in various fields of mathematics such as … claus weckerWebUffe Haagerup, University of Southern Denmark (Odense), Invariant Subspaces for Operators in II 1 Factors. Vaughan Jones, UC Berkeley, Shanks Lecture: A Trip to the Subfactor Circus. Mini-Coures: A Short Course in Planar Algebra. Narutaka Ozawa, University of Tokyo and UCLA, Hyperbolic Groups and Type II 1 Factors. Sorin Popa, … download surface laptop go driversWebWe show that this is not the case: in particular, one of the fusion categories coming from the Haagerup subfactor and one coming from the newly constructed extended Haagerup subfactor cannot be completely defined over a cyclotomic field. claus walterWebThe Haagerup subfactor is the smallest index finite depth subfactor which does not occur in one of these families. In this paper we construct the planar algebra associated … claus von wagner liveWebSep 24, 2016 · The classification of subfactors of small index revealed several new subfactors. The first subfactor above index 4, the Haagerup subfactor, is increasingly well understood and appears to lie in a… Expand 15 PDF View 2 excerpts, references background and methods SimpleC*-algebra generated by isometries J. Cuntz … clausvonwilhem robloxWebThe Haagerup subfactor is the smallest index finite-depth subfactor which does not occur in one of these families. In this paper we construct the planar algebra associated to the … download surface laptop goWebTo date, the best way of constructing these subfactors is to stumble upon a finite bipartite graph which doesn't appear as a fusion graph determine if it can be a principal … claus waidtløw