Braided groups and algebraic quantum field theories

DOI10.1007/BF00403542zbMath0745.16019OpenAlexW2020424183WikidataQ125351556 ScholiaQ125351556MaRDI QIDQ1182264

Shahn Majid

Publication date: 28 June 1992

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

Full work available at URL: https://doi.org/10.1007/bf00403542

zbMATH Keywords

quantum groupalgebraic quantum field theorysupergroupbraid statisticsbraided group of internal symmetries

Mathematics Subject Classification ID

Related Items (47)

Quantum and braided-Lie algebras ⋮ Structures of adjoint-stable algebras over factorizable Hopf algebras ⋮ Transmutation theory and rank for quantum braided groups ⋮ Quantum and braided ZX calculus* ⋮ DIAGRAMMATICS OF BRAIDED GROUP GAUGE THEORY ⋮ \(q\)-Lorentz group and braided coaddition on \(q\)-Minkowski space ⋮ THE NICHOLS ALGEBRA OF SCREENINGS ⋮ Free braided differential calculus, braided binomial theorem, and the braided exponential map ⋮ Braided Hopf algebras and differential calculus ⋮ Quasi-\(*\) structure on \(q\)-Poincaré algebras ⋮ Interrelations between quantum groups and reflection equation (braided) algebras ⋮ Examples of braided groups and braided matrices ⋮ Reconstruction of weak quasi Hopf algebras ⋮ q-epsilon tensor for quantum and braided spaces ⋮ Crossed modules, quantum braided groups, and ribbon structures ⋮ Quantized braided groups ⋮ On the addition of quantum matrices ⋮ Smash coproduct and braided groups in braided monoidal category ⋮ Random walk and the heat equation on superspace and anyspace ⋮ q-Euclidean space and quantum Wick rotation by twisting ⋮ Duality for infinite-dimensional braided bialgebras and their (co)modules ⋮ Nonstandard quantum groups and superization ⋮ Twisting algebras using non-commutative torsors: explicit computations. ⋮ Transmutation theory of a coquasitriangular weak Hopf algebra. ⋮ Braided groups and quantum groupoids. ⋮ Crossed products by a coalgebra ⋮ Nonabelian statistics for Calogero-Sutherland systems of particles. ⋮ Study of Lorentz violation in INTEGRAL gamma-ray bursts ⋮ Quantized braided linear algebras relating to quantized braided groups ⋮ Representations of U¯qsℓ(2|1) at even roots of unity ⋮ Characterization of quasi-Yetter–Drinfeld modules ⋮ Braided momentum in the q-Poincaré group ⋮ Quantum and braided linear algebra ⋮ Quantum Invariants of Templates ⋮ On the structure of irreducible Yetter-Drinfeld modules over quasi-triangular Hopf algebras ⋮ Reflection equation algebras, coideal subalgebras, and their centres ⋮ Classification of bicovariant differential calculi ⋮ Relative Yetter-Drinfeld modules and comodules over braided groups ⋮ Quantum and braided group Riemannian geometry ⋮ Quantum and braided diffeomorphism groups ⋮ Quantum doubles in monoidal categories ⋮ Centers of braided tensor categories ⋮ Extended TQFTs from non-semisimple modular categories ⋮ AN ALGEBRAIC APPROACH TO SYMMETRIC PRE-MONOIDAL STATISTICS ⋮ Braided matrix structure of the Sklyanin algebra and of the quantum Lorentz group ⋮ The braided Heisenberg group ⋮ The quantum double as quantum mechanics

Cites Work

• A new duality theory for compact groups
• Why there is a field algebra with a compact gauge group describing the superselection structure in particle physics
• Quasi-quantum groups as internal symmetries of topological quantum field theories
• Duality and quantum groups
• Braided tensor categories
• Index of subfactors and statistics of quantum fields. I
• Superselection sectors with braid group statistics and exchange algebras
• QUASITRIANGULAR HOPF ALGEBRAS AND YANG-BAXTER EQUATIONS
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