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Haagerup subfactor

Weba subfactor. The same approach was used in [17] to construct, and thoroughly analyze, the D 2n planar algebra. The rst new subfactor constructed in this way was the extended Haagerup subfactor [1]. As in the E 8 case, the D 2n planar algebra is de ned by a single uncappable generator and a list of relations, including a braiding relation of the ... WebSep 30, 2024 · Abstract. We compute the modular data (that is, the S and T matrices) for the centre of the extended Haagerup subfactor [ BMPS12 ]. The full structure (i.e., the …

[2101.04154] Microscopic Models for Fusion Categories

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 … WebThe 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 … my pillow twin size mattress topper https://wylieboatrentals.com

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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. 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). WebIn [AH99] Asaeda and Haagerup constructed two “exotic” subfactors, which were the first examples of subfactors not coming from groups or quantum groups in an … the second coming.exe stick figure download

Existence of the AH +2 subfactor

Category:A PLANAR ALGEBRA CONSTRUCTION OF THE HAAGERUP …

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Haagerup subfactor

arXiv:1609.07604v2 [math.OA] 6 Oct 2016

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- Webof a subfactor N ⊂ M is given by theory of bimodules. A subfactor N ⊂ M gives a bimodule NMN. (We should actually take a Hilbert space completion of M.) We take a relative tensor power of NMN and look at irreducible N-N bimodules arising in this way. If we have only finitely many such bimodules, we say the subfactor is of finite depth.

Haagerup subfactor

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WebWe 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. 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.

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 http://web.math.ku.dk/~haagerup/index.php?show=all

WebSep 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 … 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 …

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 …

WebThe 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 ... the second commandment isWebFeb 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 … my pillow unsubscribeWebTo 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 ... my pillow uk discount code