Elementary Bialgebra Properties of Group Rings and Enveloping Rings: An Introduction to Hopf Algebras
| Autor: | D. S. Passman |
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| Rok vydání: | 2014 |
| Předmět: | |
| Zdroj: | Communications in Algebra. 42:2222-2253 |
| ISSN: | 1532-4125 0092-7872 |
| DOI: | 10.1080/00927872.2012.753604 |
| Popis: | This is a slight extension of an expository paper I wrote a while ago as a supplement to my joint work with Declan Quinn on Burnside's theorem for Hopf algebras. It was never published, but may still be of interest to students and beginning researchers. Let K be a field, and let A be an algebra over K. Then the tensor product A ⊗ A = A ⊗ K A is also a K-algebra, and it is quite possible that there exists an algebra homomorphism Δ: A → A ⊗ A. Such a map Δ is called a comultiplication, and the seemingly innocuous assumption on its existence provides A with a good deal of additional structure. For example, using Δ, one can define a tensor product on the collection of A-modules, and when A and Δ satisfy some rather mild axioms, then A is called a bialgebra. Classical examples of bialgebras include group rings K[G] and Lie algebra enveloping rings U(L). Indeed, most of this paper is devoted to a relatively self-contained study of some elementary bialgebra properties of these examples. Furthermore, Δ determines... |
| Databáze: | OpenAIRE |
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