By Michiel Hazewinkel
The most target of this e-book is to give an creation to and functions of the idea of Hopf algebras. The authors additionally talk about a few very important features of the speculation of Lie algebras. the 1st bankruptcy may be seen as a primer on Lie algebras, with the most aim to give 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 subsequent chapters also are "primers" on coalgebras and Hopf algebras, respectively; they target in particular to offer adequate history on those themes to be used typically a part of the ebook. Chapters 4-7 are dedicated to 4 of the main appealing Hopf algebras at present identified: the Hopf algebra of symmetric services, the Hopf algebra of representations of the symmetric teams (although those are isomorphic, they're very assorted within the features 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 purposes of Hopf algebras in lots of diversified elements of arithmetic and physics. distinct gains of the booklet comprise a brand new approach to introduce Hopf algebras and coalgebras, an intensive dialogue of the various common houses of the functor of the Witt vectors, an intensive dialogue of duality features of all of the Hopf algebras pointed out, emphasis at the combinatorial features of Hopf algebras, and a survey of functions already pointed out. The e-book additionally comprises an intensive (more than seven-hundred entries) bibliography.
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