scholarly journals Prime decomposition of modular tensor categories of local modules of type D

2020 ◽  
Vol 11 (3) ◽  
pp. 489-524
Author(s):  
Andrew Schopieray
Keyword(s):  
Prime Decomposition ◽  
Tensor Categories ◽  
Type D ◽  
Modular 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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