Algebraic Geometry

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

By Michiel Hazewinkel

The most target of this booklet is to offer an advent to and purposes of the idea of Hopf algebras. The authors additionally talk about a few vital features of the speculation of Lie algebras. the 1st bankruptcy may be seen as a primer on Lie algebras, with the most target to provide 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 publication shape. the subsequent chapters also are "primers" on coalgebras and Hopf algebras, respectively; they target in particular to provide enough history on those subject matters to be used more often than not a part of the booklet. Chapters 4-7 are dedicated to 4 of the main attractive Hopf algebras presently recognized: the Hopf algebra of symmetric features, the Hopf algebra of representations of the symmetric teams (although those are isomorphic, they're very diversified within the elements they bring about to the forefront), the Hopf algebras of the nonsymmetric and quasisymmetric capabilities (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 components of arithmetic and physics. exact good points of the booklet contain a brand new solution to introduce Hopf algebras and coalgebras, an in depth dialogue of the numerous 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 points of Hopf algebras, and a survey of functions already pointed out. The e-book additionally comprises an in depth (more than seven hundred entries) bibliography.

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