Bullivant, A, Kimball, A, Martin, P et al. (1 more author) (2020) Representations of the Necklace Braid Group: Topological and Combinatorial Approaches. Communications in Mathematical Physics, 375 (2). pp. 1223-1247. ISSN 0010-3616
Abstract
The necklace braid group NBn is the motion group of the n+1 component necklace link Ln in Euclidean R3. Here Ln consists of n pairwise unlinked Euclidean circles each linked to an auxiliary circle. Partially motivated by physical considerations, we study representations of the necklace braid group NBn, especially those obtained as extensions of representations of the braid group Bn and the loop braid group LBn. We show that any irreducible Bn representation extends to NBn in a standard way. We also find some non-standard extensions of several well-known Bn-representations such as the Burau and LKB representations. Moreover, we prove that any local representation of Bn (i.e., coming from a braided vector space) can be extended to NBn, in contrast to the situation with LBn. We also discuss some directions for future study from categorical and physical perspectives.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2019, Springer Nature. This is an author produced version of an article published in Communications in Mathematical Physics. Uploaded in accordance with the publisher's self-archiving policy. |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 07 May 2019 12:57 |
Last Modified: | 06 May 2020 13:57 |
Status: | Published |
Publisher: | Springer |
Identification Number: | 10.1007/s00220-019-03445-0 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:145674 |