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Finite Quantum Groups and Cartan Matrices

✍ Scribed by Nicolás Andruskiewitsch; Hans-Jürgen Schneider

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
296 KB
Volume
154
Category
Article
ISSN
0001-8708

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✦ Synopsis

We consider a class of Hopf algebras having as an invariant a generalized Cartan matrix. For a Hopf algebra of this kind, we prove that it is finite dimensional if and only if its generalized Cartan matrix is actually a finite Cartan matrix (under some mild hypothesis). These results allow us to classify all the finite dimensional coradically graded pointed Hopf algebras whose coradical has odd prime dimension p. We also characterize coradically graded pointed Hopf algebras of order p 4 . 2000

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