Algebraic Operads : An Algorithmic Companion

Algebraic Operads: An Algorithmic Companion presents a systematic treatment of Gr bner bases in several contexts. The book builds up to the theory of Gr bner 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 Gr bner bases and their applications to the construction of universal enveloping algebras; Gr bner bases for shuffle algebras which can be used to solve questions about combinatorics of permutations; and operadic Gr bner bases, important for applications to algebraic topology, and homological and homotopical algebra. The last chapters of the book combine classical commutative Gr bner 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.