✦ LIBER ✦

Forms of Coalgebras and Hopf Algebras

✍ Scribed by Darren B. Parker

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 237 KB
Volume: 239
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.2000.8678

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✦ Synopsis

We study forms of coalgebras and Hopf algebras i.e., coalgebras and Hopf . algebras which are isomorphic after a suitable extension of the base field . We classify all forms of grouplike coalgebras according to the structure of their simple subcoalgebras. For Hopf algebras, given a W *-Galois field extension K : L for W a finite-dimensional semisimple Hopf algebra and a K-Hopf algebra H, we show w x W that all L-forms of H are invariant rings L m H under appropriate actions of W on L m H. We apply this result to enveloping algebras, duals of finite-dimensional Hopf algebras, and adjoint actions of finite-dimensional semisimple cocommutative Hopf algebras.

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