Generalisations of Hecke algebras from loop braid groups

DOI10.2140/pjm.2023.323.31arXiv2008.04840OpenAlexW4378938820MaRDI QIDQ6041523

Paul P. Martin, Celeste Damiani, Eric C. Rowell

Publication date: 31 May 2023

Published in: Pacific Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2008.04840

zbMATH Keywords

charge conservationHecke algebraloop braid group

Mathematics Subject Classification ID

Hecke algebras and their representations (20C08) Braid groups; Artin groups (20F36) Yang-Baxter equations (16T25) Braided monoidal categories and ribbon categories (18M15)

Cites Work

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• The generic representation theory of the Juyumaya algebra of braids and ties.
• Localization of unitary braid group representations
• A finiteness property for braided fusion categories
• On classification of modular tensor categories
• A \(q\)-analogue of \(U(\mathfrak{gl}(N+1))\), Hecke algebra, and the Yang-Baxter equation
• Hecke algebra representations of braid groups and link polynomials
• Hecke algebras of type \(A_ n\) and subfactors
• The Kauffman polynomial of links and representation theory
• Quantum field theory and the Jones polynomial
• The theory of motion groups
• Free fermions and the Alexander-Conway polynomial
• The blob algebra and the periodic Temperley-Lieb algebra
• On the group of conjugating automorphisms of a free group
• Über Zopfgruppen und gleichsinnig verdrillte Verkettungen
• The two-eigenvalue problem and density of Jones representation of braid groups.
• Simulation of topological field theories by quantum computers
• The braid-permutation group
• Configuration spaces of rings and wickets
• The Burau representation is not faithful for \(n=5\)
• On a canonical lift of Artin's representation to loop braid groups
• Representations of the loop braid group and Aharonov-Bohm like effects in discrete \((3+1)\)-dimensional higher gauge theory
• Representations of the necklace braid group: topological and combinatorial approaches
• On the group of ring motions of an H-trivial link
• The Burau representation is not faithful for \(n\geq 6\)
• A journey through loop braid groups
• Braid presentation of virtual knots and welded knots
• Exotic statistics for strings in 4d BF theory
• Theory of braids
• Some remarks on algebras over an algebraically closed field
• Representations of motion groups of links via dimension reduction of TQFTs
• Graded solutions of the Yang-Baxter relation and link polynomials
• EXTENDING REPRESENTATIONS OF BRAID GROUPS TO THE AUTOMORPHISM GROUPS OF FREE GROUPS
• Two paradigms for topological quantum computation
• A new polynomial invariant of knots and links
• Temperley-Lieb algebra, group theory and the Potts model
• Motion of links in the 3-sphere.
• The Burau representation of the braid group 𝐵_{𝑛} is unfaithful for large 𝑛
• AN ALGEBRAIC APPROACH TO VERTEX MODELS AND TRANSFER MATRIX SPECTRA
• ON SCHUR-WEYL DUALITY, A_n HECKE ALGEBRAS AND QUANTUM sl(N) ON $\otimes^{n+1}{\mathbb C}^N$
• A TEMPLATE FOR QUANTUM SPIN CHAIN SPECTRA
• ON HOMOLOGY OF VIRTUAL BRAIDS AND BURAU REPRESENTATION
• Burau representation for n = 4
• An Invariant of Regular Isotopy
• Braids, Link Polynomials and a New Algebra
• Topological quantum computation
• Alexander invariants of ribbon tangles and planar algebras
• Mathematics of topological quantum computing
• Generalized and Quasi-Localizations of Braid Group Representations
• Braid Groups
• On a theorem of V. I. arnol'd
• Relations between the ‘percolation’ and ‘colouring’ problem and other graph-theoretical problems associated with regular planar lattices: some exact results for the ‘percolation’ problem
• Knot Invariants and the Critical Statistical Systems

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