Nichols algebras naturally appear in the classification of finite dimensional
pointed Hopf algebras. Assuming only that the base field has characteristic
zero several new finite dimensional rank 2 Nichols algebras of diagonal type
are listed. Each of them is described in terms of generators and relations. A
Poincaré--Birkhoff--Witt basis of all of these Nichols algebras is given and
their dimension is computed. Together with the continuation of this paper this
gives an answer to a question of Andruskiewitsch.
Key Words: Hopf algebra, Lyndon words, full binary tree
%0 Generic
%1 citeulike:84414
%A Heckenberger, I.
%D 2004
%K algebras diagonal nichols
%T Finite dimensional rank 2 Nichols algebras of diagonal type I: Examples
%U http://arxiv.org/abs/math.QA/0402350
%X Nichols algebras naturally appear in the classification of finite dimensional
pointed Hopf algebras. Assuming only that the base field has characteristic
zero several new finite dimensional rank 2 Nichols algebras of diagonal type
are listed. Each of them is described in terms of generators and relations. A
Poincaré--Birkhoff--Witt basis of all of these Nichols algebras is given and
their dimension is computed. Together with the continuation of this paper this
gives an answer to a question of Andruskiewitsch.
Key Words: Hopf algebra, Lyndon words, full binary tree
@misc{citeulike:84414,
abstract = {Nichols algebras naturally appear in the classification of finite dimensional
pointed Hopf algebras. Assuming only that the base field has characteristic
zero several new finite dimensional rank 2 Nichols algebras of diagonal type
are listed. Each of them is described in terms of generators and relations. A
Poincar\'e--Birkhoff--Witt basis of all of these Nichols algebras is given and
their dimension is computed. Together with the continuation of this paper this
gives an answer to a question of Andruskiewitsch.
Key Words: Hopf algebra, Lyndon words, full binary tree},
added-at = {2007-08-18T13:22:24.000+0200},
author = {Heckenberger, I.},
biburl = {https://www.bibsonomy.org/bibtex/26a9c0e5571065355b57812bdb418b14c/a_olympia},
citeulike-article-id = {84414},
description = {citeulike},
eprint = {math.QA/0402350},
interhash = {05e7d111b910b05fbe8c90f7c3ef9c90},
intrahash = {6a9c0e5571065355b57812bdb418b14c},
keywords = {algebras diagonal nichols},
month = {April},
priority = {2},
timestamp = {2007-08-18T13:22:54.000+0200},
title = {Finite dimensional rank 2 Nichols algebras of diagonal type I: Examples},
url = {http://arxiv.org/abs/math.QA/0402350},
year = 2004
}