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

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.

Show description

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

Similar Algebraic Geometry books

Analytic K-Homology (Oxford Mathematical Monographs)

This paintings attracts jointly rules from algebraic topology, sensible research and geometry. it's a software - a way of conveying info between those 3 topics - and it's been used with luck to find theorems throughout a large span of arithmetic. the aim of this ebook is to acquaint the reader with the fundamental rules of analytic K-homology and advance a few of its functions.

The Geometry of Topological Stability (London Mathematical Society Monographs)

In featuring a close research of the geometry and topology of various periods of "generic" singularities, Geometry of Topological balance bridges the distance among algebraic calculations and continuity arguments to element the mandatory and adequate stipulations for a C (infinity) to be C]0-stable. all through, the authors masterfully research this significant topic utilizing effects culled from a large diversity of mathematical disciplines, together with geometric topology, stratification thought, algebraic geometry, and commutative algebra.

Lectures on Polytopes (Graduate Texts in Mathematics)

In line with a graduate path on the Technische Universit├Ąt, Berlin, those lectures current a wealth of fabric at the sleek thought of convex polytopes. the simple exposition gains many illustrations, and entire proofs for many theorems. With in simple terms linear algebra as a prerequisite, it takes the reader speedy from the fundamentals to subject matters of contemporary learn.

Higher-Dimensional Algebraic Geometry (Universitext)

The category conception of algebraic forms is the point of interest of this e-book. This very lively quarter of study remains to be constructing, yet an awesome volume of data has gathered over the last 20 years. The authors aim is to supply an simply obtainable creation to the topic. The e-book begins with preparatory and traditional definitions and effects, then strikes directly to speak about a variety of points of the geometry of delicate projective forms with many rational curves, and finishes in taking the 1st steps in the direction of Moris minimum version application of class of algebraic types via proving the cone and contraction theorems.

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

Show sample text content

Rated 4.78 of 5 – based on 35 votes