Download E-books Algebras, Rings and Modules: Lie Algebras and Hopf Algebras (Mathematical Surveys and Monographs) PDF

By Michiel Hazewinkel

The most objective of this e-book is to offer an advent to and functions of the idea of Hopf algebras. The authors additionally speak about a few vital points of the idea of Lie algebras. the 1st bankruptcy could be considered as a primer on Lie algebras, with the most objective to provide an explanation for and turn out the Gabriel-Bernstein-Gelfand-Ponomarev theorem at the correspondence among the representations of Lie algebras and quivers; this fabric has now not formerly seemed in publication shape. the following chapters also are "primers" on coalgebras and Hopf algebras, respectively; they target in particular to offer enough heritage on those themes to be used usually a part of the ebook. Chapters 4-7 are dedicated to 4 of the main appealing Hopf algebras at the moment identified: the Hopf algebra of symmetric services, the Hopf algebra of representations of the symmetric teams (although those are isomorphic, they're very various within the points they bring about to the forefront), the Hopf algebras of the nonsymmetric and quasisymmetric services (these are twin and either generalize the former two), and the Hopf algebra of variations. The final bankruptcy is a survey of functions of Hopf algebras in lots of diverse components of arithmetic and physics. targeted beneficial properties of the e-book contain a brand new option to introduce Hopf algebras and coalgebras, an in depth dialogue of the various common houses of the functor of the Witt vectors, a radical dialogue of duality elements of all of the Hopf algebras pointed out, emphasis at the combinatorial facets of Hopf algebras, and a survey of purposes already pointed out. The booklet additionally includes an intensive (more than seven hundred entries) bibliography.

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