Low-dimensional representations of the three component loop braid group

DOI10.1063/1.4935361zbMath1331.20045arXiv1508.00005OpenAlexW2108878737MaRDI QIDQ3457150

Julia Yael Plavnik, Paul Bruillard, Michael Sun, Seung-Moon Hong, Eric C. Rowell, Liang Chang

Publication date: 10 December 2015

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1508.00005

zbMATH Keywords

braid groupsirreducible representationsstandard extension of representations

Mathematics Subject Classification ID

Ordinary representations and characters (20C15) Braid groups; Artin groups (20F36)

Related Items (6)

A journey through loop braid groups ⋮ Representations of the necklace braid group: topological and combinatorial approaches ⋮ Representations of the loop braid groups from braided tensor categories ⋮ The features of the spacetime ⋮ Representations of the necklace braid group \(\mathcal{NB}_n\) of dimension 4 \((n=2,3,4)\) ⋮ Mathematics of topological quantum computing

Uses Software

• Magma

Cites Work

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• Dense families of \(B_3\)-representations and braid reversion.
• The theory of motion groups
• The Magma algebra system. I: The user language
• Virtual knot theory
• A modular functor which is universal for quantum computation
• Exotic statistics for strings in 4d BF theory
• LOCAL REPRESENTATIONS OF THE LOOP BRAID GROUP
• EXTENDING REPRESENTATIONS OF BRAID GROUPS TO THE AUTOMORPHISM GROUPS OF FREE GROUPS
• Coefficients of the Characteristic Polynomial
• THE IRREDUCIBLE COMPLEX REPRESENTATIONS OF THE BRAID GROUP ON n STRINGS OF DEGREE ≤ n
• FORBIDDEN MOVES UNKNOT A VIRTUAL KNOT
• ON HOMOLOGY OF VIRTUAL BRAIDS AND BURAU REPRESENTATION
• Topological quantum computation
• Braid groups are linear
• Representations of the braid group \(B_3\) and of \(\text{SL}(2,\mathbb{Z})\).

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