Algebraic Operads

· Grundlehren der mathematischen Wissenschaften Livre 346 · Springer Science & Business Media
E-book
636
Pages
Les notes et avis ne sont pas vérifiés. En savoir plus

À propos de cet e-book

In many areas of mathematics some “higher operations” are arising. These havebecome so important that several research projects refer to such expressions. Higher operationsform new types of algebras. The key to understanding and comparing them, to creating invariants of their action is operad theory. This is a point of view that is 40 years old in algebraic topology, but the new trend is its appearance in several other areas, such as algebraic geometry, mathematical physics, differential geometry, and combinatorics. The present volume is the first comprehensive and systematic approach to algebraic operads. An operad is an algebraic device that serves to study all kinds of algebras (associative, commutative, Lie, Poisson, A-infinity, etc.) from a conceptual point of view. The book presents this topic with an emphasis on Koszul duality theory. After a modern treatment of Koszul duality for associative algebras, the theory is extended to operads. Applications to homotopy algebra are given, for instance the Homotopy Transfer Theorem. Although the necessary notions of algebra are recalled, readers are expected to be familiar with elementary homological algebra. Each chapter ends with a helpful summary and exercises. A full chapter is devoted to examples, and numerous figures are included.

After a low-level chapter on Algebra, accessible to (advanced) undergraduate students, the level increases gradually through the book. However, the authors have done their best to make it suitable for graduate students: three appendices review the basic results needed in order to understand the various chapters. Since higher algebra is becoming essential in several research areas like deformation theory, algebraic geometry, representation theory, differential geometry, algebraic combinatorics, and mathematical physics, the book can also be used as a reference work by researchers.

À propos de l'auteur

Jean-Louis Loday has worked in algebraic K-theory, algebraic topology, noncommutative geometry and higher algebra. He is the author of "Cyclic Homology" a worldwide reference, published as volume 301 in the Grundleheren der mathematischen Wissenschadften. He is an editor of several mathematical journals and several Proceedings. He has organized six of the annual conferences "Operads 20xx" (starting in 2004).

Bruno Vallette has worked on operads since his first years in mathematical research. He is the author of 10 research articles and a specialist of properads and of Batalin-Vilkovisky algebras.

Loday and Vallette organized several summer schools and international conferences on the subject (France, China, Norway) and published the Proceedings of these conferences.

Donner une note à cet e-book

Dites-nous ce que vous en pensez.

Informations sur la lecture

Smartphones et tablettes
Installez l'application Google Play Livres pour Android et iPad ou iPhone. Elle se synchronise automatiquement avec votre compte et vous permet de lire des livres en ligne ou hors connexion, où que vous soyez.
Ordinateurs portables et de bureau
Vous pouvez écouter les livres audio achetés sur Google Play à l'aide du navigateur Web de votre ordinateur.
Liseuses et autres appareils
Pour lire sur des appareils e-Ink, comme les liseuses Kobo, vous devez télécharger un fichier et le transférer sur l'appareil en question. Suivez les instructions détaillées du Centre d'aide pour transférer les fichiers sur les liseuses compatibles.