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 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 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

HOPF ALGEBRAS OF DIMENSION 30

2010 ◽  
Vol 09 (01) ◽  
pp. 11-15 ◽  
Author(s):  
DAIJIRO FUKUDA
Keyword(s):  
Hopf Algebra ◽  
Group Algebra ◽  
Hopf Algebras ◽  
Characteristic Zero ◽  
Closed Field ◽  
Algebraically Closed Field ◽  
Finite Dimensional

This paper contributes to the classification of finite dimensional Hopf algebras. It is shown that every Hopf algebra of dimension 30 over an algebraically closed field of characteristic zero is semisimple and thus isomorphic to a group algebra or the dual of a group algebra.

scholarly journals On the Classification of Strongly Graded Hopf Algebras

2002 ◽  
Vol 251 (1) ◽  
pp. 358-370 ◽  
Author(s):  
Antonio M. Cegarra
Keyword(s):  
Hopf Algebras

scholarly journals Classification of singular spinor fields and other mass dimension one fermions

2014 ◽  
Vol 23 (14) ◽  
pp. 1444002 ◽  
Author(s):  
R. T. Cavalcanti
Keyword(s):  
Spinor Field ◽  
General Classification ◽  
Constraint Equations ◽  
Spinor Fields ◽  
Mass Dimension ◽  
Dimension One ◽  
Elko Spinor Fields

In this paper, we investigate the constraint equations of the Lounesto spinor fields classification and show that it can be used to completely characterize all the singular classes, which can potentially accommodate further mass dimension one fermions, beyond the well known Elko spinor fields. This result can be useful for two purposes: Besides a great abridgement in the classification of a given spinor field, we provide a general form of each class of spinor fields, which can be used furthermore to search for a general classification of spinors dynamics.

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