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- W4287996105 abstract "A few years ago the so-called oriented subgroup $vec F$ of the Thompson group $F$ was introduced by V. Jones while investigating the connections between subfactors and conformal field theories. In the coding of links and knots by elements of $F$ it corresponds exactly to the oriented ones. Thanks to the work of Golan and Sapir, $vec F$ provided the first example of a maximal subgroup of infinite index in $F$ different from the parabolic subgroups that fix a point in $(0,1)$. In this paper we investigate possible analogues of $vec F$ in higher Thompson groups $F_k, kgeq 2$, with $F=F_2$, introduced by Brown. Most notably, we study algebraic properties of the oriented subgroup $vec{F}_3$ of $F_3$, as described recently by Jones, and prove in particular that it gives rise to a non-parabolic maximal subgroup of infinite index in $F_3$ and that the corresponding quasi-regular representation is irreducible." @default.
- W4287996105 created "2022-07-26" @default.
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- W4287996105 date "2019-12-10" @default.
- W4287996105 modified "2023-10-16" @default.
- W4287996105 title "On the oriented Thompson subgroup $vec{F}_3$ and its relatives in higher Brown-Thompson groups" @default.
- W4287996105 hasPublicationYear "2019" @default.
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