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Algebra structures coming from tangles. (English) Zbl 1408.57009

Morrison, Scott (ed.) et al., Proceedings of the 2014 Maui and 2015 Qinhuangdao conferences in honour of Vaughan F. R. Jones’ 60th birthday. Canberra: Australian National University, Centre for Mathematics and its Applications. Proc. Cent. Math. Appl. Aust. Natl. Univ. 46, 379-383 (2017).
Summary: In an attempt to find analogues, for higher relative commutants, of the Bose-Mesner algebra structure on the second relative commutant of a spin-model subfactor, we find that there do indeed exist other algebra structures on the higher relative commutants of any subfactor planar algebra which are induced by the action of tangles; in fact, we show they can only arise in the obvious fashion.
For the entire collection see [Zbl 1386.46002].

MSC:

57M25 Knots and links in the \(3\)-sphere (MSC2010)
81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations
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Full Text: Euclid