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