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Hopf algebras of low dimension

✍ Scribed by Dragoş Ştefan

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
962 KB
Volume
211
Category
Article
ISSN
0021-8693

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✦ Synopsis

The main aim of this paper is to classify all types of Hopf algebras of dimension less thn or equal to 11 over an algebraically closed field of characteristic 0. If A is such a Hopf algebra that is not semisimple, then we shall prove that A or A* is pointed. This property will result from the fact that, under some assumptions, any Hopf algebra that is generated as an algebra by a four-dimensional simple subcoalgebra is a Hopf quotient of the coordinate ring of quantum SL2(k). The first result allows us to reduce the classification to the case of pointed Hopf algebras of dimension 8. We shall describe their types in the last part of the paper.

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