Representations of a class of positively based algebras

Shiyu Lin; Shilin Yang

Czechoslovak Mathematical Journal (2023)

  • Volume: 73, Issue: 3, page 811-838
  • ISSN: 0011-4642

Abstract

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We investigate the representation theory of the positively based algebra A m , d , which is a generalization of the noncommutative Green algebra of weak Hopf algebra corresponding to the generalized Taft algebra. It turns out that A m , d is of finite representative type if d ≤ 4 , of tame type if d = 5 , and of wild type if d ≥ 6 . In the case when d ≤ 4 , all indecomposable representations of A m , d are constructed. Furthermore, their right cell representations as well as left cell representations of A m , d are described.

How to cite

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Lin, Shiyu, and Yang, Shilin. "Representations of a class of positively based algebras." Czechoslovak Mathematical Journal 73.3 (2023): 811-838. <http://eudml.org/doc/299120>.

@article{Lin2023,
abstract = {We investigate the representation theory of the positively based algebra $A_\{m,d\}$, which is a generalization of the noncommutative Green algebra of weak Hopf algebra corresponding to the generalized Taft algebra. It turns out that $A_\{m,d\}$ is of finite representative type if $d\le 4$, of tame type if $d=5$, and of wild type if $d\ge 6.$ In the case when $d\le 4$, all indecomposable representations of $A_\{m,d\}$ are constructed. Furthermore, their right cell representations as well as left cell representations of $A_\{m,d\}$ are described.},
author = {Lin, Shiyu, Yang, Shilin},
journal = {Czechoslovak Mathematical Journal},
keywords = {positively based algebra; indecomposable module; cell module},
language = {eng},
number = {3},
pages = {811-838},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Representations of a class of positively based algebras},
url = {http://eudml.org/doc/299120},
volume = {73},
year = {2023},
}

TY - JOUR
AU - Lin, Shiyu
AU - Yang, Shilin
TI - Representations of a class of positively based algebras
JO - Czechoslovak Mathematical Journal
PY - 2023
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 73
IS - 3
SP - 811
EP - 838
AB - We investigate the representation theory of the positively based algebra $A_{m,d}$, which is a generalization of the noncommutative Green algebra of weak Hopf algebra corresponding to the generalized Taft algebra. It turns out that $A_{m,d}$ is of finite representative type if $d\le 4$, of tame type if $d=5$, and of wild type if $d\ge 6.$ In the case when $d\le 4$, all indecomposable representations of $A_{m,d}$ are constructed. Furthermore, their right cell representations as well as left cell representations of $A_{m,d}$ are described.
LA - eng
KW - positively based algebra; indecomposable module; cell module
UR - http://eudml.org/doc/299120
ER -

References

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