On the origin and development of subfactors and quantum topology

Abstract

Abstract. We give an account of the beginning of subfactor theory and TQFT and some more recent developments.

Rigidity results for von Neumann algebras arising from mixing extensions of profinite actions of groups on probability spaces

“…In his seminal paper [Jo81] Jones pioneered the study of inclusions of type II 1 factors, or subfactors. Subfactor theory has had a number of striking applications over the years in various diverse branches of mathematics and mathematical physics, including Knot theory and Conformal Field theory, [Jo90,Jo91,Jo09]. A major motivating question in Subfactor theory is the classification of all intermediate subalgebras.…”

Interpolated family of non group-like simple integral fusion rings of Lie type

“…The original motivations of this work are in subfactor theory [17]. A subfactor encodes a Galois-like quantum generalization of the notion of symmetry [12,19], analogous to a field extension, where its planar algebra [18] and its fusion category [8] are the analogous of the Galois group and its representation category, respectively. The index of a subfactor is multiplicative with its intermediates, so a subfactor without proper intermediate (called a maximal subfactor [1]) can be seen as a quantum analogous of the notion of prime number (about a quantum analogous of the notion of natural number, see [32][33][34]).…”