scholarly journals Prime regular Hopf algebras of GK-dimension one

2010 ◽  
Vol 101 (1) ◽  
pp. 260-302 ◽  
Author(s):  
K. A. Brown ◽  
J. J. Zhang
Keyword(s):  
Hopf Algebras ◽  
Dimension One ◽  
Gk Dimension

scholarly journals Classification of affine prime regular Hopf algebras of GK-dimension one

2016 ◽  
Vol 296 ◽  
pp. 1-54 ◽  
Author(s):  
Jinyong Wu ◽  
Gongxiang Liu ◽  
Nanqing Ding
Keyword(s):  
Hopf Algebras ◽  
Dimension One ◽  
Gk Dimension

The Grothendieck rings of Wu–Liu–Ding algebras and their Casimir numbers (I)

2021 ◽  
pp. 2250178
Author(s):  
Ruifang Yang ◽  
Shilin Yang
Keyword(s):  
Hopf Algebras ◽  
Commutative Rings ◽  
New Class ◽  
Grothendieck Rings ◽  
Dimension One ◽  
Gk Dimension

Wu–Liu–Ding algebras are a class of affine prime regular Hopf algebras of GK-dimension one, denoted by [Formula: see text]. In this paper, we consider their quotient algebras [Formula: see text] which are a new class of non-pointed semisimple Hopf algebras. We describe the Grothendieck rings of [Formula: see text] when [Formula: see text] is odd. It turns out that the Grothendieck rings are commutative rings generated by three elements subject to some relations. Then we compute the Casimir numbers of the Grothendieck rings for [Formula: see text] and [Formula: see text].

scholarly journals Representations of a non-pointed Hopf algebra

2021 ◽  
Vol 6 (10) ◽  
pp. 10523-10539
Author(s):  
Ruifang Yang ◽  
◽  
Shilin Yang
Keyword(s):  
Hopf Algebra ◽  
Tensor Product ◽  
Hopf Algebras ◽  
Indecomposable Modules ◽  
Representation Ring ◽  
Pointed Hopf Algebras ◽  
Dimension One ◽  
Gk Dimension

<abstract><p>In this paper, we construct all the indecomposable modules of a class of non-pointed Hopf algebras, which are quotient Hopf algebras of a class of prime Hopf algebras of GK-dimension one. Then the decomposition formulas of the tensor product of any two indecomposable modules are established. Based on these results, the representation ring of the Hopf algebras is characterized by generators and some relations.</p></abstract>

scholarly journals Hopf algebras of GK-dimension two with vanishing Ext-group

2013 ◽  
Vol 388 ◽  
pp. 219-247 ◽  
Author(s):  
D.-G. Wang ◽  
J.J. Zhang ◽  
G. Zhuang
Keyword(s):  
Hopf Algebras ◽  
Gk Dimension

scholarly journals AFFINE SEMIPRIME ALGEBRAS OF GK DIMENSION ONE ARE (STILL) PI

2003 ◽  
Vol 45 (2) ◽  
pp. 243-247 ◽  
Author(s):  
CHRISTOPHER J. PAPPACENA ◽  
LANCE W. SMALL ◽  
JEANNE WALD
Keyword(s):  
Dimension One ◽  
Gk Dimension

Left counital Hopf algebras on bi-decorated planar rooted forests and Rota-Baxter systems

2020 ◽  
Vol 27 (2) ◽  
pp. 219-243 ◽  
Author(s):  
Xiao-Song Peng ◽  
Yi Zhang ◽  
Xing Gao ◽  
Yan-Feng Luo
Keyword(s):  
Hopf Algebras

scholarly journals Monadic cointegrals and applications to quasi-Hopf algebras

2021 ◽  
Vol 225 (10) ◽  
pp. 106678
Author(s):  
Johannes Berger ◽  
Azat M. Gainutdinov ◽  
Ingo Runkel
Keyword(s):  
Hopf Algebras
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