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portada Algebraic Operads: An Algorithmic Companion
Type
Physical Book
Publisher
Author
Language
English
Pages
384
Format
Paperback
ISBN13
9781032921082
Edition No.
1

Algebraic Operads: An Algorithmic Companion

Murray R. Bremner; Vladimir Dotsenko (Author) · Crc Press · Paperback

Algebraic Operads: An Algorithmic Companion - Murray R. Bremner; Vladimir Dotsenko

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Synopsis "Algebraic Operads: An Algorithmic Companion"

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