## 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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