The bicrossed products of H 4 and H 8

Daowei Lu; Yan Ning; Dingguo Wang

Czechoslovak Mathematical Journal (2020)

  • Volume: 70, Issue: 4, page 959-977
  • ISSN: 0011-4642

Abstract

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Let H 4 and H 8 be the Sweedler’s and Kac-Paljutkin Hopf algebras, respectively. We prove that any Hopf algebra which factorizes through H 8 and H 4 (equivalently, any bicrossed product between the Hopf algebras H 8 and H 4 ) must be isomorphic to one of the following four Hopf algebras: H 8 ⊗ H 4 , H 32 , 1 , H 32 , 2 , H 32 , 3 . The set of all matched pairs ( H 8 , H 4 , ▹ , ◃ ) is explicitly described, and then the associated bicrossed product is given by generators and relations.

How to cite

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Lu, Daowei, Ning, Yan, and Wang, Dingguo. "The bicrossed products of $H_4$ and $H_8$." Czechoslovak Mathematical Journal 70.4 (2020): 959-977. <http://eudml.org/doc/297368>.

@article{Lu2020,
abstract = {Let $H_4$ and $H_8$ be the Sweedler’s and Kac-Paljutkin Hopf algebras, respectively. We prove that any Hopf algebra which factorizes through $H_8$ and $H_4$ (equivalently, any bicrossed product between the Hopf algebras $H_8$ and $H_4$) must be isomorphic to one of the following four Hopf algebras: $H_8\otimes H_4,H_\{32,1\},H_\{32,2\},H_\{32,3\}$. The set of all matched pairs $(H_8,H_4,\triangleright ,\triangleleft )$ is explicitly described, and then the associated bicrossed product is given by generators and relations.},
author = {Lu, Daowei, Ning, Yan, Wang, Dingguo},
journal = {Czechoslovak Mathematical Journal},
keywords = {Kac-Paljutkin Hopf algebra; Sweedler's Hopf algebra; bicrossed product; factorization problem},
language = {eng},
number = {4},
pages = {959-977},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The bicrossed products of $H_4$ and $H_8$},
url = {http://eudml.org/doc/297368},
volume = {70},
year = {2020},
}

TY - JOUR
AU - Lu, Daowei
AU - Ning, Yan
AU - Wang, Dingguo
TI - The bicrossed products of $H_4$ and $H_8$
JO - Czechoslovak Mathematical Journal
PY - 2020
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 70
IS - 4
SP - 959
EP - 977
AB - Let $H_4$ and $H_8$ be the Sweedler’s and Kac-Paljutkin Hopf algebras, respectively. We prove that any Hopf algebra which factorizes through $H_8$ and $H_4$ (equivalently, any bicrossed product between the Hopf algebras $H_8$ and $H_4$) must be isomorphic to one of the following four Hopf algebras: $H_8\otimes H_4,H_{32,1},H_{32,2},H_{32,3}$. The set of all matched pairs $(H_8,H_4,\triangleright ,\triangleleft )$ is explicitly described, and then the associated bicrossed product is given by generators and relations.
LA - eng
KW - Kac-Paljutkin Hopf algebra; Sweedler's Hopf algebra; bicrossed product; factorization problem
UR - http://eudml.org/doc/297368
ER -

References

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