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.
Read Online or Download Algebras, Rings and Modules: Lie Algebras and Hopf Algebras (Mathematical Surveys and Monographs) PDF
Best Algebraic Geometry books
Fractal styles have emerged in lots of contexts, yet what precisely is a development? How can one make distinctive the constructions mendacity inside of items and the relationships among them? This booklet proposes new notions of coherent geometric constitution to supply a clean method of this well-known box. It develops a brand new notion of self-similarity referred to as "BPI" or "big items of itself," which makes the sector a lot more uncomplicated for individuals to go into.
The speculation of elliptic curves is exotic through its lengthy historical past and by means of the range of the equipment which have been utilized in its research. This ebook treats the mathematics method in its smooth formula, by utilizing easy algebraic quantity thought and algebraic geometry. Following a quick dialogue of the mandatory algebro-geometric effects, the booklet proceeds with an exposition of the geometry and the formal crew of elliptic curves, elliptic curves over finite fields, the complicated numbers, neighborhood fields, and worldwide fields.
This publication introduces the speculation of modular types, from which all rational elliptic curves come up, with a watch towards the Modularity Theorem. dialogue covers elliptic curves as complicated tori and as algebraic curves; modular curves as Riemann surfaces and as algebraic curves; Hecke operators and Atkin-Lehner concept; Hecke eigenforms and their mathematics homes; the Jacobians of modular curves and the Abelian forms linked to Hecke eigenforms.
Additional resources for Algebras, Rings and Modules: Lie Algebras and Hopf Algebras (Mathematical Surveys and Monographs)