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.

Show description

Read or Download Algebras, Rings and Modules: Lie Algebras and Hopf Algebras (Mathematical Surveys and Monographs) PDF

Best Algebraic Geometry books

An Introduction to Algebraic Geometry and Algebraic Groups (Oxford Graduate Texts in Mathematics)

An obtainable textual content introducing algebraic geometries and algebraic teams at complicated undergraduate and early graduate point, this e-book develops the language of algebraic geometry from scratch and makes use of it to establish the idea of affine algebraic teams from first rules. development at the history fabric from algebraic geometry and algebraic teams, the textual content presents an creation to extra complicated and specialized fabric.

The Arithmetic of Elliptic Curves (Graduate Texts in Mathematics)

The speculation of elliptic curves is amazing by way of its lengthy heritage and by means of the range of the equipment which were utilized in its learn. This e-book treats the mathematics process in its smooth formula, by using easy algebraic quantity conception and algebraic geometry. Following a short dialogue of the mandatory algebro-geometric effects, the e-book proceeds with an exposition of the geometry and the formal workforce of elliptic curves, elliptic curves over finite fields, the advanced numbers, neighborhood fields, and international fields.

Foundations of Hyperbolic Manifolds (Graduate Texts in Mathematics)

This seriously class-tested publication is an exposition of the theoretical foundations of hyperbolic manifolds. it's a either a textbook and a reference. A easy wisdom of algebra and topology on the first yr graduate point of an American college is thought. the 1st half is worried with hyperbolic geometry and discrete teams.

Extra resources for Algebras, Rings and Modules: Lie Algebras and Hopf Algebras (Mathematical Surveys and Monographs)

Show sample text content

Rated 4.12 of 5 – based on 34 votes