scholarly journals From quantum groups to unitary modular tensor categories

2006 ◽  
pp. 215-230 ◽  
Author(s):  
Eric C. Rowell
Keyword(s):  
Quantum Groups ◽  
Tensor Categories ◽  
Modular Tensor Categories

scholarly journals Quivers, Quasi-Quantum Groups and Finite Tensor Categories

2011 ◽  
Vol 303 (3) ◽  
pp. 595-612 ◽  
Author(s):  
Hua-Lin Huang ◽  
Gongxiang Liu ◽  
Yu Ye
Keyword(s):  
Quantum Groups ◽  
Tensor Categories

scholarly journals L2-Betti numbers of rigid C∗-tensor categories and discrete quantum groups

2017 ◽  
Vol 10 (7) ◽  
pp. 1757-1791 ◽  
Author(s):  
David Kyed ◽  
Sven Raum ◽  
Stefaan Vaes ◽  
Matthias Valvekens
Keyword(s):  
Quantum Groups ◽  
Betti Numbers ◽  
Tensor Categories

scholarly journals Witness algebra and anyon braiding

2020 ◽  
Vol 30 (3) ◽  
pp. 234-270
Author(s):  
Andreas Blass ◽  
Yuri Gurevich
Keyword(s):  
Quantum Computation ◽  
Category Theory ◽  
Two Dimensional ◽  
Mathematical Basis ◽  
Tensor Categories ◽  
Topological Quantum ◽  
Modular Tensor Categories ◽  
Topological Quantum Computation

AbstractTopological quantum computation employs two-dimensional quasiparticles called anyons. The generally accepted mathematical basis for the theory of anyons is the framework of modular tensor categories. That framework involves a substantial amount of category theory and is, as a result, considered rather difficult to understand. Is the complexity of the present framework necessary? The computations of associativity and braiding matrices can be based on a much simpler framework, which looks less like category theory and more like familiar algebra. We introduce that framework here.

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