Hopf Algebras which Factorize through the Taft Algebra Tm2(q) and the Group Hopf Algebra K[Cn]

被引：3

作者：

Agore, Ana-Loredana ^{[1
,2
]}

机构：

[1] Vrije Univ Brussel, Fac Engn, Pl Laan 2, B-1050 Brussels, Belgium

[2] Romanian Acad, Simion Stoilow Inst Math, POB 1-764, Bucharest 014700, Romania

来源：

SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS | 2018年 / 14卷

关键词：

bicrossed product; the factorization problem; classification of Hopf algebras; CLASSIFYING BICROSSED PRODUCTS; FINITE-GROUPS; RANK-ONE; CONSTRUCTION; EXTENSIONS;

D O I：

10.3842/SIGMA.2018.027

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We completely describe by generators and relations and classify all Hopf algebras which factorize through the Taft algebra T-m2(q) and the group Hopf algebra K[C-n]: they are nm(2)-dimensional quantum groups T-nm2(omega)(q) associated to an n-th root of unity omega. Furthermore, using Dirichlet's prime number theorem we are able to count the number of isomorphism types of such Hopf algebras. More precisely, if d = gcd(m, nu(n)) and nu(n)/d = p(1)(alpha 1)...p(r)(alpha r) is the prime decomposition of nu(n)/d then the number of types of Hopf algebras that factorize through T-m2(q) and K[C-n] is equal to (alpha(1) + 1)(alpha(2) + 1)...(alpha(r) + 1), where nu(n) is the order of the group of n-th roots of unity in K. As a consequence of our approach, the automorphism groups of these Hopf algebras are described as well.

引用

页数：14