scholarly journals On rigidity of Nichols algebras

2015 ◽  
Vol 219 (12) ◽  
pp. 5539-5559 ◽  
Author(s):  
Iván Angiono ◽  
Mikhail Kochetov ◽  
Mitja Mastnak
Keyword(s):  
Nichols Algebras

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.

scholarly journals Nichols algebras of group type with many quadratic relations

2011 ◽  
Vol 227 (5) ◽  
pp. 1956-1989 ◽  
Author(s):  
M. Graña ◽  
I. Heckenberger ◽  
L. Vendramin
Keyword(s):  
Group Type ◽  
Nichols Algebras

EXT ALGEBRA OF NICHOLS ALGEBRAS OF CARTAN TYPE A2

2013 ◽  
Vol 12 (04) ◽  
pp. 1250191
Author(s):  
XIAOLAN YU ◽  
YINHUO ZHANG
Keyword(s):  
Spectral Sequence ◽  
Hopf Algebras ◽  
Type A ◽  
Serre Spectral Sequence ◽  
Nichols Algebra ◽  
Cartan Type ◽  
Dynkin Diagrams ◽  
Full Structure ◽  
Pointed Hopf Algebras ◽  
Nichols Algebras

We give the full structure of the Ext algebra of any Nichols algebra of Cartan type A2 by using the Hochschild–Serre spectral sequence. As an application, we show that the pointed Hopf algebras [Formula: see text] with Dynkin diagrams of type A, D, or E, except for A1 and A1 × A1 with the order NJ > 2 for at least one component J, are wild.

scholarly journals Nichols algebras with standard braiding

2009 ◽  
Vol 3 (1) ◽  
pp. 35-106 ◽  
Author(s):  
Iván Angiono
Keyword(s):  
Nichols Algebras

scholarly journals Nichols algebras over groups with finite root system of rank two I

2010 ◽  
Vol 324 (11) ◽  
pp. 3090-3114 ◽  
Author(s):  
I. Heckenberger ◽  
H.-J. Schneider
Keyword(s):  
Root System ◽  
Nichols Algebras

scholarly journals A Freeness Theorem for Nichols Algebras

2000 ◽  
Vol 231 (1) ◽  
pp. 235-257 ◽  
Author(s):  
Matías Graña
Keyword(s):  
Nichols Algebras

scholarly journals On Nichols Algebras with Generic Braiding

2008 ◽  
pp. 47-64 ◽  
Author(s):  
Nicolás Andruskiewitsch ◽  
Iván Ezequiel Angiono
Keyword(s):  
Nichols Algebras

scholarly journals Finite-dimensional Nichols algebras over dual Radford algebras

2020 ◽  
pp. 2140001
Author(s):  
O. Márquez ◽  
D. Bagio ◽  
J. M. J. Giraldi ◽  
G. A. García
Keyword(s):  
Jorge Luis Borges ◽  
Drinfeld Modules ◽  
Indecomposable Modules ◽  
Simple Modules ◽  
Generators And Relations ◽  
Dimension Formula ◽  
Finite Dimensional ◽  
Nichols Algebras ◽  
The Way

For [Formula: see text], let [Formula: see text] be the dual of the Radford algebra of dimension [Formula: see text]. We present new finite-dimensional Nichols algebras arising from the study of simple Yetter–Drinfeld modules over [Formula: see text]. Along the way, we describe the simple objects in [Formula: see text] and their projective envelopes. Then we determine those simple modules that give rise to finite-dimensional Nichols algebras for the case [Formula: see text]. There are 18 possible cases. We present by generators and relations, the corresponding Nichols algebras on five of these eighteen cases. As an application, we characterize finite-dimensional Nichols algebras over indecomposable modules for [Formula: see text] and [Formula: see text], [Formula: see text], which recovers some results of the second and third author in the former case, and of Xiong in the latter. Cualquier destino, por largo y complicado que sea, consta en realidad de un solo momento: el momento en que el hombre sabe para siempre quién es. Jorge Luis Borges

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