scholarly journals Quantum Grothendieck rings and derived Hall algebras

2013 ◽  
Vol 0 (0) ◽  
Author(s):  
David Hernandez ◽  
Bernard Leclerc
Keyword(s):  
Hall Algebras ◽  
Grothendieck Rings

scholarly journals An introduction to motivic Hall algebras

2012 ◽  
Vol 229 (1) ◽  
pp. 102-138 ◽  
Author(s):  
Tom Bridgeland
Keyword(s):  
Hall Algebras

scholarly journals Hall algebras and quantum Frobenius

2010 ◽  
Vol 154 (1) ◽  
pp. 181-206 ◽  
Author(s):  
Kevin Mcgerty
Keyword(s):  
Hall Algebras

scholarly journals The center of the extended Haagerup subfactor has 22 simple objects

2017 ◽  
Vol 28 (01) ◽  
pp. 1750009 ◽  
Author(s):  
Scott Morrison ◽  
Kevin Walker
Keyword(s):  
Fusion Category ◽  
Dimension Function ◽  
Fusion Ring ◽  
Fusion Categories ◽  
Modular Data ◽  
Grothendieck Rings ◽  
Combinatorial Data

We explain a technique for discovering the number of simple objects in [Formula: see text], the center of a fusion category [Formula: see text], as well as the combinatorial data of the induction and restriction functors at the level of Grothendieck rings. The only input is the fusion ring [Formula: see text] and the dimension function [Formula: see text]. In particular, we apply this to deduce that the center of the extended Haagerup subfactor has 22 simple objects, along with their decompositions as objects in either of the fusion categories associated to the subfactor. This information has been used subsequently in [T. Gannon and S. Morrison, Modular data for the extended Haagerup subfactor (2016), arXiv:1606.07165 .] to compute the full modular data. This is the published version of arXiv:1404.3955 .

scholarly journals Semistable Chow–Hall algebras of quivers and quantized Donaldson–Thomas invariants

2018 ◽  
Vol 12 (5) ◽  
pp. 1001-1025 ◽  
Author(s):  
Hans Franzen ◽  
Markus Reineke
Keyword(s):  
Hall Algebras

scholarly journals Abstract Grothendieck rings

1987 ◽  
Vol 53 (1) ◽  
pp. 17-25
Author(s):  
Kazimierz Szymiczek
Keyword(s):  
Grothendieck Rings

Gröbner-Shirshov basis for degenerate Ringel-Hall algebras of type F 4

2016 ◽  
Vol 37 (2) ◽  
pp. 199-210
Author(s):  
Zhenzhen Gao ◽  
Abdukadir Obul
Keyword(s):  
Hall Algebras
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