By Michiel Hazewinkel
The most objective of this e-book is to offer an advent to and functions of the idea of Hopf algebras. The authors additionally speak about a few vital points of the idea of Lie algebras. the 1st bankruptcy could be considered as a primer on Lie algebras, with the most objective to provide an explanation for and turn out 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 following chapters also are "primers" on coalgebras and Hopf algebras, respectively; they target in particular to offer enough heritage on those themes to be used usually a part of the ebook. Chapters 4-7 are dedicated to 4 of the main appealing Hopf algebras at the moment identified: the Hopf algebra of symmetric services, the Hopf algebra of representations of the symmetric teams (although those are isomorphic, they're very various within the points they bring about 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 variations. The final bankruptcy is a survey of functions of Hopf algebras in lots of diverse components of arithmetic and physics. targeted beneficial properties of the e-book contain a brand new option 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 facets of Hopf algebras, and a survey of purposes already pointed out. The booklet additionally includes an intensive (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
Algebraic topology is a simple a part of sleek arithmetic, and a few wisdom of this region is integral for any complex paintings on the subject of geometry, together with topology itself, differential geometry, algebraic geometry, and Lie teams. This publication offers an in depth therapy of algebraic topology either for academics of the topic and for complicated graduate scholars in arithmetic both focusing on this zone or carrying on with directly to different fields.
First textbook-level account of easy examples and methods during this zone. appropriate for self-study through a reader who is aware a bit commutative algebra and algebraic geometry already. David Eisenbud is a widely known mathematician and present president of the yankee Mathematical Society, in addition to a winning Springer writer.
Grothendieck’s attractive thought of schemes permeates sleek algebraic geometry and underlies its functions to quantity idea, physics, and utilized arithmetic. this easy account of that concept emphasizes and explains the common geometric suggestions in the back of the definitions. within the publication, suggestions are illustrated with primary examples, and specific calculations convey how the buildings of scheme conception are performed in perform.
This vintage textual content, written through one of many greatest mathematicians of the 20 th century, is now to be had in a good value paperback variation. Exposition is based at the foundations of affine geometry, the geometry of quadratic varieties, and the constitution of the overall linear crew. Context is broadened by way of the inclusion of projective and symplectic geometry and the constitution of symplectic and orthogonal teams.
Additional resources for Algebras, Rings and Modules: Lie Algebras and Hopf Algebras (Mathematical Surveys and Monographs)