Special modules for $R\left(\mathrm{PSL}\right(2,q\left)\right)$

Cao, Liufeng, and Chen, Huixiang. "Special modules for $R({\rm PSL}(2,q))$." Czechoslovak Mathematical Journal 73.4 (2023): 1301-1317. <http://eudml.org/doc/299472>.

@article{Cao2023,
abstract = {Let $R$ be a fusion ring and $R_\mathbb \{C\}:=R\otimes _\mathbb \{Z\}\mathbb \{C\}$ be the corresponding fusion algebra. We first show that the algebra $R_\mathbb \{C\}$ has only one left (right, two-sided) cell and the corresponding left (right, two-sided) cell module. Then we prove that, up to isomorphism, $R_\mathbb \{C\}$ admits a unique special module, which is 1-dimensional and given by the Frobenius-Perron homomorphism FPdim. Moreover, as an example, we explicitly determine the special module of the interpolated fusion algebra $R(\{\rm PSL\}(2,q)):=r(\{\rm PSL\}(2,q))\otimes _\mathbb \{Z\}\mathbb \{C\}$ up to isomorphism, where $r(\{\rm PSL\}(2,q))$ is the interpolated fusion ring with even $q\ge 2$.},
author = {Cao, Liufeng, Chen, Huixiang},
journal = {Czechoslovak Mathematical Journal},
keywords = {Frobenius-Perron theorem; special module; fusion ring},
language = {eng},
number = {4},
pages = {1301-1317},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Special modules for $R(\{\rm PSL\}(2,q))$},
url = {http://eudml.org/doc/299472},
volume = {73},
year = {2023},
}

TY - JOUR
AU - Cao, Liufeng
AU - Chen, Huixiang
TI - Special modules for $R({\rm PSL}(2,q))$
JO - Czechoslovak Mathematical Journal
PY - 2023
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 73
IS - 4
SP - 1301
EP - 1317
AB - Let $R$ be a fusion ring and $R_\mathbb {C}:=R\otimes _\mathbb {Z}\mathbb {C}$ be the corresponding fusion algebra. We first show that the algebra $R_\mathbb {C}$ has only one left (right, two-sided) cell and the corresponding left (right, two-sided) cell module. Then we prove that, up to isomorphism, $R_\mathbb {C}$ admits a unique special module, which is 1-dimensional and given by the Frobenius-Perron homomorphism FPdim. Moreover, as an example, we explicitly determine the special module of the interpolated fusion algebra $R({\rm PSL}(2,q)):=r({\rm PSL}(2,q))\otimes _\mathbb {Z}\mathbb {C}$ up to isomorphism, where $r({\rm PSL}(2,q))$ is the interpolated fusion ring with even $q\ge 2$.
LA - eng
KW - Frobenius-Perron theorem; special module; fusion ring
UR - http://eudml.org/doc/299472
ER -