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Algebraic Operads
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An Algorithmic Companion
Besorgungstitel - wird vorgemerkt | Lieferzeit: Besorgungstitel - Lieferbar innerhalb von 10 Werktagen I
Artikel-Nr:
9781482248562
Veröffentl:
2016
Erscheinungsdatum:
05.04.2016
Seiten:
365
Autor:
Murray R Bremner
Gewicht:
703 g
Format:
234x157x25 mm
Sprache:
Englisch
Beschreibung:
Murray R. Bremner, PhD, is a professor at the University of Saskatchewan in Canada. He attended that university as an undergraduate, and received an M. Comp. Sc. degree at Concordia University in Montréal. He obtained a doctorate in mathematics at Yale University with a thesis entitled On Tensor Products of Modules over the Virasoro Algebra. Prior to returning to Saskatchewan, he held shorter positions at MSRI in Berkeley and at the University of Toronto. Dr. Bremner authored the book Lattice Basis Reduction: An Introduction to the LLL Algorithm and Its Applications and is a co-translator with M. V. Kotchetov of Selected Works of A. I. Shirshov in English Translation. His primary research interests are algebraic operads, nonassociative algebra, representation theory, and computer algebra.
This book 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. 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.
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.