cauchy theorem
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2021 ◽  
Vol 2012 (1) ◽  
pp. 012064
Author(s):  
Jiarui Song ◽  
Zhanhua Shi ◽  
Haotao Wang
Keyword(s):  


2020 ◽  
Vol 141 (1) ◽  
pp. 411-439
Author(s):  
Peter Yuditskii


2020 ◽  
pp. 1-13
Author(s):  
ZHIHUA WANG ◽  
GONGXIANG LIU ◽  
LIBIN LI

Abstract Let $\mathcal{C}$ be a fusion category over an algebraically closed field $\mathbb{k}$ of arbitrary characteristic. Two numerical invariants of $\mathcal{C}$ , that is, the Casimir number and the determinant of $\mathcal{C}$ are considered in this paper. These two numbers are both positive integers and admit the property that the Grothendieck algebra $(\mathcal{C})\otimes_{\mathbb{Z}}K$ over any field K is semisimple if and only if any of these numbers is not zero in K. This shows that these two numbers have the same prime factors. If moreover $\mathcal{C}$ is pivotal, it gives a numerical criterion that $\mathcal{C}$ is nondegenerate if and only if any of these numbers is not zero in $\mathbb{k}$ . For the case that $\mathcal{C}$ is a spherical fusion category over the field $\mathbb{C}$ of complex numbers, these two numbers and the Frobenius–Schur exponent of $\mathcal{C}$ share the same prime factors. This may be thought of as another version of the Cauchy theorem for spherical fusion categories.





2013 ◽  
Vol 59 (1) ◽  
pp. 110-119 ◽  
Author(s):  
S.A. Plaksa ◽  
V.S. Shpakivskyi






2003 ◽  
Vol 259 (1) ◽  
pp. 87-94 ◽  
Author(s):  
Carla Dionisi ◽  
Giorgio Ottaviani
Keyword(s):  


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