scholarly journals The breaking of quantum double symmetries by defect condensation

2007 ◽  
Vol 322 (3) ◽  
pp. 552-598 ◽  
Author(s):  
F.A. Bais ◽  
C.J.M. Mathy
Keyword(s):  
Quantum Double ◽  
Double Symmetries

scholarly journals Electric-magnetic duality in twisted quantum double model of topological orders

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Yuting Hu ◽  
Yidun Wan
Keyword(s):  
Normal Subgroup ◽  
Gauge Group ◽  
The Other ◽  
Quantum Double ◽  
Duality Transformation ◽  
Abelian Normal Subgroup

Abstract We derive a partial electric-magnetic (PEM) duality transformation of the twisted quantum double (TQD) model TQD(G, α) — discrete Dijkgraaf-Witten model — with a finite gauge group G, which has an Abelian normal subgroup N , and a three-cocycle α ∈ H3(G, U(1)). Any equivalence between two TQD models, say, TQD(G, α) and TQD(G′, α′), can be realized as a PEM duality transformation, which exchanges the N-charges and N-fluxes only. Via the PEM duality, we construct an explicit isomorphism between the corresponding TQD algebras Dα(G) and Dα′(G′) and derive the map between the anyons of one model and those of the other.

Double-bosonization of braided groups and the construction of Uq(g)

1999 ◽  
Vol 125 (1) ◽  
pp. 151-192 ◽  
Author(s):  
S. MAJID
Keyword(s):  
Hopf Algebra ◽  
Quantum Groups ◽  
Cartan Subalgebra ◽  
Positive Root ◽  
Point Of View ◽  
Root Space ◽  
Quantum Double ◽  
Braided Group ◽  
Negative Root ◽  
Quasitriangular Hopf Algebra

We introduce a quasitriangular Hopf algebra or ‘quantum group’ U(B), the double-bosonization, associated to every braided group B in the category of H-modules over a quasitriangular Hopf algebra H, such that B appears as the ‘positive root space’, H as the ‘Cartan subalgebra’ and the dual braided group B* as the ‘negative root space’ of U(B). The choice B=Uq(n+) recovers Lusztig's construction of Uq(g); other choices give more novel quantum groups. As an application, our construction provides a canonical way of building up quantum groups from smaller ones by repeatedly extending their positive and negative root spaces by linear braided groups; we explicitly construct Uq(sl3) from Uq(sl2) by this method, extending it by the quantum-braided plane. We provide a fundamental representation of U(B) in B. A projection from the quantum double, a theory of double biproducts and a Tannaka–Krein reconstruction point of view are also provided.

Spatially limited quantum double well oscillator

2006 ◽  
Author(s):  
Andrey T. Bagmanov ◽  
Andrey L. Sanin
Keyword(s):  
Quantum Double
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