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Forms of pointed Hopf algebras

✍ Scribed by S. Caenepeel; S. Dăscălescu; L. Le Bruyn

Publisher
Springer
Year
1999
Tongue
English
Weight
120 KB
Volume
100
Category
Article
ISSN
0025-2611

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We give a structure theorem for pointed Hopf algebras of dimension p 3 , having coradical kC , where k is an algebraically closed field of characteristic zero. p Combining this with previous results, we obtain the complete classification of all pointed Hopf algebras of dimension p 3 .

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Some of the first examples of Hopf algebras described over a field k w x which are neither commutative nor cocommutative 13, 14 involve elements a and x which satisfy the relations ⌬ a s a m a, ⌬ x s x m a q 1 m x, and xa s qax Ž . Ž . for some q g k \_ 0. With the advent of quantum groups these re