Automorphism group of green algebra of weak Hopf algebra corresponding to Sweedler Hopf algebra

Liufeng Cao; Dong Su; Hua Yao

Czechoslovak Mathematical Journal (2023)

  • Volume: 73, Issue: 1, page 101-115
  • ISSN: 0011-4642

Abstract

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Let r ( 𝔴 2 0 ) be the Green ring of the weak Hopf algebra 𝔴 2 0 corresponding to Sweedler’s 4-dimensional Hopf algebra H 2 , and let Aut ( R ( 𝔴 2 0 ) ) be the automorphism group of the Green algebra R ( 𝔴 2 0 ) = r ( 𝔴 2 0 ) ⊗ ℤ ℂ . We show that the quotient group Aut ( R ( 𝔴 2 0 ) ) / C 2 ≅ S 3 , where C 2 contains the identity map and is isomorphic to the infinite group ( ℂ * , × ) and S 3 is the symmetric group of order 6.

How to cite

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Cao, Liufeng, Su, Dong, and Yao, Hua. "Automorphism group of green algebra of weak Hopf algebra corresponding to Sweedler Hopf algebra." Czechoslovak Mathematical Journal 73.1 (2023): 101-115. <http://eudml.org/doc/299535>.

@article{Cao2023,
abstract = {Let $r(\mathfrak \{w\}^0_2)$ be the Green ring of the weak Hopf algebra $\mathfrak \{w\}^0_2$ corresponding to Sweedler’s 4-dimensional Hopf algebra $H_2$, and let $\{\rm Aut\}(R(\mathfrak \{w\}^0_2))$ be the automorphism group of the Green algebra $R(\mathfrak \{w\}^0_2)=r(\mathfrak \{w\}^0_2)\otimes _\mathbb \{Z\}\mathbb \{C\}$. We show that the quotient group $\{\rm Aut\}(R(\mathfrak \{w\}^0_2))/C_2\cong S_3$, where $C_2$ contains the identity map and is isomorphic to the infinite group $(\mathbb \{C\}^*,\times )$ and $S_3$ is the symmetric group of order 6.},
author = {Cao, Liufeng, Su, Dong, Yao, Hua},
journal = {Czechoslovak Mathematical Journal},
keywords = {Green algebra; automorphism group; weak Hopf algebra},
language = {eng},
number = {1},
pages = {101-115},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Automorphism group of green algebra of weak Hopf algebra corresponding to Sweedler Hopf algebra},
url = {http://eudml.org/doc/299535},
volume = {73},
year = {2023},
}

TY - JOUR
AU - Cao, Liufeng
AU - Su, Dong
AU - Yao, Hua
TI - Automorphism group of green algebra of weak Hopf algebra corresponding to Sweedler Hopf algebra
JO - Czechoslovak Mathematical Journal
PY - 2023
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 73
IS - 1
SP - 101
EP - 115
AB - Let $r(\mathfrak {w}^0_2)$ be the Green ring of the weak Hopf algebra $\mathfrak {w}^0_2$ corresponding to Sweedler’s 4-dimensional Hopf algebra $H_2$, and let ${\rm Aut}(R(\mathfrak {w}^0_2))$ be the automorphism group of the Green algebra $R(\mathfrak {w}^0_2)=r(\mathfrak {w}^0_2)\otimes _\mathbb {Z}\mathbb {C}$. We show that the quotient group ${\rm Aut}(R(\mathfrak {w}^0_2))/C_2\cong S_3$, where $C_2$ contains the identity map and is isomorphic to the infinite group $(\mathbb {C}^*,\times )$ and $S_3$ is the symmetric group of order 6.
LA - eng
KW - Green algebra; automorphism group; weak Hopf algebra
UR - http://eudml.org/doc/299535
ER -

References

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