scholarly journals Representations of Hopf-Ore Extensions of Group Algebras and Pointed Hopf Algebras of Rank One

2015 ◽  
Vol 18 (3) ◽  
pp. 801-830 ◽  
Author(s):  
Zhen Wang ◽  
Lan You ◽  
Hui-Xiang Chen
Keyword(s):  
Hopf Algebras ◽  
Group Algebras ◽  
Rank One ◽  
Pointed Hopf Algebras ◽  
Ore Extensions

scholarly journals EXAMPLES OF FINITE-DIMENSIONAL POINTED HOPF ALGEBRAS IN CHARACTERISTIC 2

2020 ◽  
pp. 1-14
Author(s):  
NICOLÁS ANDRUSKIEWITSCH ◽  
DIRCEU BAGIO ◽  
SARADIA DELLA FLORA ◽  
DAIANA FLÔRES
Keyword(s):  
Hopf Algebras ◽  
Abelian Groups ◽  
Vector Spaces ◽  
Group Algebras ◽  
Finite Abelian Groups ◽  
Finite Dimensional ◽  
Pointed Hopf Algebras ◽  
Characteristic 2 ◽  
Nichols Algebras ◽  
Kirillov Dimension

Abstract We present new examples of finite-dimensional Nichols algebras over fields of characteristic 2 from braided vector spaces that are not of diagonal type, admit realizations as Yetter–Drinfeld modules over finite abelian groups, and are analogous to Nichols algebras of finite Gelfand–Kirillov dimension in characteristic 0. New finite-dimensional pointed Hopf algebras over fields of characteristic 2 are obtained by bosonization with group algebras of suitable finite abelian groups.

Ideals of Finite-Dimensional Pointed Hopf Algebras of Rank One

2021 ◽  
Vol 28 (02) ◽  
pp. 351-360
Author(s):  
Yu Wang ◽  
Zhihua Wang ◽  
Libin Li
Keyword(s):  
Hopf Algebra ◽  
Hopf Algebras ◽  
Adjoint Action ◽  
Prime Ideals ◽  
Closed Field ◽  
Finite Dimensional ◽  
Maximal Ideals ◽  
Primitive Ideals ◽  
Rank One ◽  
Pointed Hopf Algebras

Let [Formula: see text] be a finite-dimensional pointed Hopf algebra of rank one over an algebraically closed field of characteristic zero. In this paper we show that any finite-dimensional indecomposable [Formula: see text]-module is generated by one element. In particular, any indecomposable submodule of [Formula: see text] under the adjoint action is generated by a special element of [Formula: see text]. Using this result, we show that the Hopf algebra [Formula: see text] is a principal ideal ring, i.e., any two-sided ideal of [Formula: see text] is generated by one element. As an application, we give explicitly the generators of ideals, primitive ideals, maximal ideals and completely prime ideals of the Taft algebras.

scholarly journals CLASSIFICATION OF QUIVER HOPF ALGEBRAS AND POINTED HOPF ALGEBRAS OF TYPE ONE

2012 ◽  
Vol 87 (2) ◽  
pp. 216-237
Author(s):  
SHOUCHUAN ZHANG ◽  
HUI-XIANG CHEN ◽  
YAO-ZHONG ZHANG
Keyword(s):  
Hopf Algebras ◽  
Irreducible Representations ◽  
Group Algebras ◽  
Pointed Hopf Algebras ◽  
Nichols Algebras

AbstractQuiver Hopf algebras are classified by means of ramification systems with irreducible representations. This leads to the classification of Nichols algebras over group algebras and pointed Hopf algebras of type one.

scholarly journals HOPF IMAGES AND INNER FAITHFUL REPRESENTATIONS

2010 ◽  
Vol 52 (3) ◽  
pp. 677-703 ◽  
Author(s):  
TEODOR BANICA ◽  
JULIEN BICHON
Keyword(s):  
Lie Algebras ◽  
Hopf Algebras ◽  
Discrete Group ◽  
Faithful Representation ◽  
Group Algebras ◽  
Enveloping Algebras ◽  
Algebra Representation ◽  
Function Algebras ◽  
Pointed Hopf Algebras ◽  
Tannaka Duality

AbstractWe develop a general theory of Hopf image of a Hopf algebra representation, with the associated concept of inner faithful representation, modelled on the notion of faithful representation of a discrete group. We study several examples, including group algebras, enveloping algebras of Lie algebras, pointed Hopf algebras, function algebras, twistings and cotwistings, and we present a Tannaka duality formulation of the notion of Hopf image.

scholarly journals Constructing Pointed Hopf Algebras by Ore Extensions

2000 ◽  
Vol 225 (2) ◽  
pp. 743-770 ◽  
Author(s):  
M Beattie ◽  
S Dăscălescu ◽  
L Grünenfelder
Keyword(s):  
Hopf Algebras ◽  
Pointed Hopf Algebras ◽  
Ore Extensions

scholarly journals Bialgebra cohomology, pointed Hopf algebras, and deformations

2009 ◽  
Vol 213 (7) ◽  
pp. 1399-1417 ◽  
Author(s):  
Mitja Mastnak ◽  
Sarah Witherspoon
Keyword(s):  
Hopf Algebras ◽  
Pointed Hopf Algebras
Sign in / Sign up

Export Citation Format

Share Document