scholarly journals Tannaka–Kreıˇn reconstruction and a characterization of modular tensor categories

2009 ◽  
Vol 321 (12) ◽  
pp. 3714-3763 ◽  
Author(s):  
Hendryk Pfeiffer
Keyword(s):  
Tensor Categories ◽  
Modular Tensor Categories

scholarly journals Pointed finite tensor categories over abelian groups

2017 ◽  
Vol 28 (11) ◽  
pp. 1750087
Author(s):  
Iván Angiono ◽  
César Galindo
Keyword(s):  
Abelian Group ◽  
Cohomology Class ◽  
Hopf Algebras ◽  
Abelian Groups ◽  
Tensor Category ◽  
Tensor Categories ◽  
Finite Dimensional ◽  
Pointed Hopf Algebras

We give a characterization of finite pointed tensor categories obtained as de-equivariantizations of the category of corepresentations of finite-dimensional pointed Hopf algebras with abelian group of group-like elements only in terms of the (cohomology class of the) associator of the pointed part. As an application we prove that every coradically graded pointed finite braided tensor category is a de-equivariantization of the category of corepresentations of a finite-dimensional pointed Hopf algebras with abelian group of group-like elements.

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.

Sign in / Sign up

Export Citation Format

Share Document