scholarly journals Finite GK-dimensional pre-Nichols algebras of quantum linear spaces and of Cartan type

2021 ◽  
Vol 8 (10) ◽  
pp. 296-329
Author(s):  
Nicolás Andruskiewitsch ◽  
Guillermo Sanmarco
Keyword(s):  
Linear Spaces ◽  
Cartan 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 Liftings of Nichols algebras of diagonal type III. Cartan type G 2

2017 ◽  
Vol 478 ◽  
pp. 506-568 ◽  
Author(s):  
Agustín García Iglesias ◽  
João Matheus Jury Giraldi
Keyword(s):  
Cartan Type ◽  
Type Iii ◽  
Nichols Algebras

scholarly journals Liftings of Nichols Algebras of Diagonal Type I. Cartan Type A

2016 ◽  
pp. rnw103 ◽  
Author(s):  
Nicolás Andruskiewitsch ◽  
Iván Angiono ◽  
Agustín García Iglesias
Keyword(s):  
Type A ◽  
Type I ◽  
Cartan Type ◽  
Nichols Algebras

Operator approach for orthogonality in linear spaces

2018 ◽  
Vol 11 (4) ◽  
pp. 103-112
Author(s):  
Mahdi Iranmanesh ◽  
Maryam Saeedi Khojasteh
Keyword(s):  
Operator Approach ◽  
Linear Spaces

Sub-normed Z-linear Spaces on Commutative Semi-group

2012 ◽  
Vol 14 (2) ◽  
pp. 157
Author(s):  
Yanqiu WANG ◽  
Huaxin ZHAO
Keyword(s):  
Semi Group ◽  
Linear Spaces
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