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Hochschild Cohomology and the Coradical Filtration of Pointed Coalgebras: Applications

✍ Scribed by Dragoş Ştefan; Freddy Van Oystaeyen

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 181 KB
Volume: 210
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1998.7594

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✦ Synopsis

In this paper we show that there is a close connection between the coradical filtration of a pointed coalgebra and the Hochschild cohomology of that coalgebra with coefficients in some one-dimensional bicomodules. As an application, for a given prime number p and an algebraically closed field k of characteristic 0, we classify all pointed Hopf algebras of dimension p 3 over k.

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✍ Darren B. Parker 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 127 KB

We investigate the coradical filtration of pointed coalgebras. First, we generalize a theorem of Taft and Wilson using techniques developed by Radford. We then look at the coradical filtration of duals of inseparable field extensions L \* upon extension of the base field K, where K ⊆ L is a field ex