By Michiel Hazewinkel
The most aim of this ebook is to provide an advent to and functions of the speculation of Hopf algebras. The authors additionally talk about a few vital points of the idea of Lie algebras. the 1st bankruptcy should be considered as a primer on Lie algebras, with the most objective to give an explanation for and end up 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 e-book shape. the subsequent chapters also are "primers" on coalgebras and Hopf algebras, respectively; they target particularly to provide enough history on those themes to be used broadly speaking a part of the publication. Chapters 4-7 are dedicated to 4 of the main appealing Hopf algebras at the moment identified: the Hopf algebra of symmetric features, the Hopf algebra of representations of the symmetric teams (although those are isomorphic, they're very various within the features they carry to the forefront), the Hopf algebras of the nonsymmetric and quasisymmetric features (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 assorted components of arithmetic and physics. precise good points of the booklet contain a brand new method to introduce Hopf algebras and coalgebras, an intensive dialogue of the various common homes of the functor of the Witt vectors, an intensive dialogue of duality facets of the entire Hopf algebras pointed out, emphasis at the combinatorial facets of Hopf algebras, and a survey of purposes already pointed out. The booklet additionally comprises an in depth (more than seven hundred entries) bibliography.
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