By Michiel Hazewinkel
The most objective of this e-book is to give an creation to and functions of the speculation of Hopf algebras. The authors additionally speak about a few very important features of the speculation of Lie algebras. the 1st bankruptcy might 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 ebook shape. the following chapters also are "primers" on coalgebras and Hopf algebras, respectively; they target in particular to offer adequate heritage on those subject matters to be used basically a part of the e-book. Chapters 4-7 are dedicated to 4 of the main appealing Hopf algebras presently recognized: the Hopf algebra of symmetric capabilities, the Hopf algebra of representations of the symmetric teams (although those are isomorphic, they're very diverse within the elements they create 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 diversifications. The final bankruptcy is a survey of purposes of Hopf algebras in lots of different components of arithmetic and physics. certain gains of the ebook comprise a brand new method 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 features of Hopf algebras, and a survey of functions already pointed out. The ebook additionally includes an in depth (more than seven hundred entries) bibliography.
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