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Azumaya algebras and artin's theorem

✍ Scribed by W Schelter


Publisher
Elsevier Science
Year
1977
Tongue
English
Weight
90 KB
Volume
46
Category
Article
ISSN
0021-8693

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Let \(H\) be a finite dimensional cocommutative Hopf algebra over a field \(K\) of characteristic zero. Then it is possible for \(H\) to be simple; that is, \(H\) has no proper nontrivial subHopf algebras. In particular, the Hopf algebraic analog of Artin's theorem for representations of finite grou

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An algebra \(R\) with anti-isomorphism ( \({ }^{*}\) ) is shown to be Azumaya if (*) is given by an element of \(R \otimes R^{\text {op }}\); in particular, this is the case if the canonical map \(R \otimes_{C} R^{\text {op }} \rightarrow \operatorname{End}_{C}(R)\) is onto. Consequently, the existe