Algebraic Operads

Algebraic Operads: An Algorithmic Companion presents a systematic treatment of Grbner bases in several contexts. The book builds up to the theory of Grbner bases for operads due to the second author and Khoroshkin as well as various applications of the corresponding diamond lemmas in algebra. The authors present a variety of topics including: noncommutative Grbner bases and their applications to the construction of universal enveloping algebras; Grbner bases for shuffle algebras which can be used to solve questions about combinatorics of permutations; and operadic Grbner bases, important for applications to algebraic topology, and homological and homotopical algebra. The last chapters of the book combine classical commutative Grbner bases with operadic ones to approach some classification problems for operads. 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.