On the Linearized Artin Braid Representation
F. Constantinescu, F. Toppan
TL;DR
This paper introduces a linear faithful representation of the braid group via automorphisms of a free group, extending it to colored and pure braid groups, with applications in two-dimensional physics.
Contribution
It generalizes the linearization of the Artin braid representation to colored and pure braid groups, providing new tools for mathematical and physical applications.
Findings
Established a linear faithful representation of the braid group
Extended the representation to colored and pure braid groups
Discussed applications in two-dimensional physics
Abstract
We linearize the Artin representation of the braid group given by (right) automorphisms of a free group providing a linear faithful representation of the braid group. This result is generalized to obtain linear representations for the coloured braid groupoid and pure braid group too. Applications to some areas of two-dimensional physics are discussed.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsSpectral Theory in Mathematical Physics