Haagerup subfactor
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 … 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 ...
Haagerup subfactor
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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). 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 ...
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. WebFeb 20, 2012 · We prove that the Brauer-Picard group of Morita autoequiv- alences of each of the three fusion categories which arise as an even part of the Asaeda-Haagerup subfactor or of its index 2 extension is the Klein four-group. We describe the 36 bimodule categories which occur in the full subgroupoid of the Brauer-Picard groupoid on these …
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 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 … current jobs at caritas fort portalWebMar 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. current jobs at taso ugandaWebThe 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 … current job opportunity at td bankWebUffe 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, … charly perfumeWebThe 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 ... charly phildarWebSep 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 … charly picotWebHaagerup’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 charly picot cucq