Algebraic Operads - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Algebraic Operads write by Jean-Louis Loday. This book was released on 2012-08-08. Algebraic Operads available in PDF, EPUB and Kindle. 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.
Operads in Algebra, Topology and Physics
Operads in Algebra, Topology and Physics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Operads in Algebra, Topology and Physics write by Martin Markl. This book was released on 2002. Operads in Algebra, Topology and Physics available in PDF, EPUB and Kindle. Operads are mathematical devices which describe algebraic structures of many varieties and in various categories. From their beginnings in the 1960s, they have developed to encompass such areas as combinatorics, knot theory, moduli spaces, string field theory and deformation quantization.
Algebraic Operads
Algebraic Operads - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Algebraic Operads write by Murray R. Bremner. This book was released on 2016-04-06. Algebraic Operads available in PDF, EPUB and Kindle. This book presents a systematic treatment of Grobner bases in several contexts. The book builds up to the theory of Grobner bases for operads due to the second author and Khoroshkin as well as various applications of the corresponding diamond lemmas in algebra. Throughout the book, both the mathematical theory and computational methods are emphasized and numerous algorithms, examples, and exercises are provided to clarify and illustrate the concrete meaning of abstract theory.
Colored Operads
Colored Operads - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Colored Operads write by Donald Yau. This book was released on 2016-02-29. Colored Operads available in PDF, EPUB and Kindle. The subject of this book is the theory of operads and colored operads, sometimes called symmetric multicategories. A (colored) operad is an abstract object which encodes operations with multiple inputs and one output and relations between such operations. The theory originated in the early 1970s in homotopy theory and quickly became very important in algebraic topology, algebra, algebraic geometry, and even theoretical physics (string theory). Topics covered include basic graph theory, basic category theory, colored operads, and algebras over colored operads. Free colored operads are discussed in complete detail and in full generality. The intended audience of this book includes students and researchers in mathematics and other sciences where operads and colored operads are used. The prerequisite for this book is minimal. Every major concept is thoroughly motivated. There are many graphical illustrations and about 150 exercises. This book can be used in a graduate course and for independent study.
Operads and Universal Algebra
Operads and Universal Algebra - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Operads and Universal Algebra write by Chengming Bai. This book was released on 2012. Operads and Universal Algebra available in PDF, EPUB and Kindle. The book aims to exemplify the recent developments in operad theory, in universal algebra and related topics in algebraic topology and theoretical physics. The conference has established a better connection between mathematicians working on operads (mainly the French team) and mathematicians working in universal algebra (primarily the Chinese team), and to exchange problems, methods and techniques from these two subject areas.
