tensor categories
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2021 ◽  
Vol 225 (9) ◽  
pp. 106705
Author(s):  
Petter Andreas Bergh ◽  
Julia Yael Plavnik ◽  
Sarah Witherspoon

2021 ◽  
Vol 21 (4) ◽  
pp. 2107-2140
Author(s):  
Adrien Brochier ◽  
David Jordan ◽  
Pavel Safronov ◽  
Noah Snyder
Keyword(s):  

2021 ◽  
pp. 2150077
Author(s):  
Vaughan F. R. Jones ◽  
Jun Yang

We discuss the structure of the Motzkin algebra [Formula: see text] by introducing a sequence of idempotents and the basic construction. We show that [Formula: see text] admits a factor trace if and only if [Formula: see text] and the higher commutants of these factors depend on [Formula: see text]. Then a family of irreducible bimodules over these factors is constructed. A tensor category with [Formula: see text] fusion rule is obtained from these bimodules.


2021 ◽  
Vol 157 (7) ◽  
pp. 1584-1609
Author(s):  
Kevin Coulembier

We prove a constructive existence theorem for abelian envelopes of non-abelian monoidal categories. This establishes a new tool for the construction of tensor categories. As an example we obtain new proofs for the existence of several universal tensor categories as conjectured by Deligne. Another example constructs interesting tensor categories in positive characteristic via tilting modules for ${\rm SL}_2$ .


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