Zobrazeno 1 - 10
of 203
pro vyhledávání: '"Bigelow, Stephen"'
Autor:
Bigelow, Stephen, Martel, Jules
We reconstruct a quantum group associated with any Lie algebra together with its representation theory from twisted homologies of generalized configuration spaces of disks. Along the way it brings new combinatorics to the theory, but our diagrams rep
Externí odkaz:
http://arxiv.org/abs/2405.06982
Autor:
Bigelow, Stephen
The $SL_n$ spider gives a diagrammatic way to encode the representation category of the quantum group $U_q(sl_n)$. The aim of this paper is to define a new spider that contains the $SL_n$ spider. The new spider is defined by generators and relations,
Externí odkaz:
http://arxiv.org/abs/1808.10575
Autor:
Bigelow, Stephen, Levaillant, Claire
Fibonacci anyons are attractive for use in topological quantum computation because any unitary transformation of their state space can be approximated arbitrarily accurately by braiding. However there is no known braid that entangles two qubits witho
Externí odkaz:
http://arxiv.org/abs/1802.01011
Autor:
Grano, Ellie, Bigelow, Stephen
The Jones-Wenzl idempotents are elements of the Temperley-Lieb planar algebra that are important, but complicated to write down. We will present a new planar algebra, the pop-switch planar algebra, which contains the Temperley-Lieb planar algebra. It
Externí odkaz:
http://arxiv.org/abs/1501.04672
Autor:
Bigelow, Stephen
In a remark in his seminal 1987 paper, Jones describes a way to define the Burau matrix of a positive braid using a metaphor of bowling a ball down a bowling alley with braided lanes. We extend this definition to allow multiple bowling balls to be bo
Externí odkaz:
http://arxiv.org/abs/1409.4074
Autor:
Bigelow, Stephen
We give a diagrammatic definition of $U_q(sl_2)$ when $q$ is not a root of unity, including its Hopf algebra structure and its relationship with the Temperley-Lieb category.
Externí odkaz:
http://arxiv.org/abs/1308.1071
Autor:
Bigelow, Stephen, Penneys, David
We show that if the principal graph of a subfactor planar algebra of modulus \delta>2 is stable for two depths, then it must end in A_{finite} tails. This result is analogous to Popa's theorem on principal graph stability. We use these theorems to sh
Externí odkaz:
http://arxiv.org/abs/1208.1564
Autor:
Bigelow, Stephen
We give a new construction of the one-variable Alexander polynomial of an oriented knot or link, and show that it generalizes to a vector valued invariant of oriented tangles.
Comment: 8 pages
Comment: 8 pages
Externí odkaz:
http://arxiv.org/abs/1203.5457
A tangle is an oriented 1-submanifold of the cylinder whose endpoints lie on the two disks in the boundary of the cylinder. Using an algebraic tool developed by Lescop, we extend the Burau representation of braids to a functor from the category of or
Externí odkaz:
http://arxiv.org/abs/1203.4590
In the 1920's Artin defined the braid group in an attempt to understand knots in a more algebraic setting. A braid is a certain arrangement of strings in three-dimensional space. It is a celebrated theorem of Alexander that every knot is obtainable f
Externí odkaz:
http://arxiv.org/abs/1110.0538