Algebraic Operads: An Algorithmic Companion

ISBN-13: 9781482248562 / Angielski / Twarda / 2016 / 365 str.

Murray R. Bremner; Vladimir Dotsenko

Opis

Algebraic Operads: An Algorithmic Companion 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. The authors present a variety of topics including: noncommutative Grobner bases and their applications to the construction of universal enveloping algebras; Grobner bases for shuffle algebras which can be used to solve questions about combinatorics of permutations; and operadic Grobner bases, important for applications to algebraic topology, and homological and homotopical algebra. The last chapters of the book combine classical commutative Grobner 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."

Spis treści

Normal Forms for Vectors and Univariate Polynomials. Noncommutative Associative Algebras. Nonsymmetric Operads. Twisted Associative Algebras and Shuffle Algebras. Symmetric Operads and Shuffle Operads. Operadic Homological Algebra and Gröbner Bases. Commutative Gröbner Bases. Linear Algebra over Polynomial Rings. Case Study of Nonsymmetric Binary Cubic Operads. Case Study of Nonsymmetric Ternary Quadratic Operads. Appendices: Maple Code for Buchberger’s Algorithm.