Free Delivery Over $100
|
|
|||
|
||||
OverviewAlgebraic 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. Full Product DetailsAuthor: Murray R. Bremner , Vladimir DotsenkoPublisher: Taylor & Francis Inc Imprint: Chapman & Hall/CRC Dimensions: Width: 15.60cm , Height: 2.50cm , Length: 23.40cm Weight: 0.684kg ISBN: 9781482248562ISBN 10: 1482248565 Pages: 365 Publication Date: 05 April 2016 Audience: College/higher education , College/higher education , Professional and scholarly , Undergraduate , Postgraduate, Research & Scholarly Format: Hardback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsReviewsThis book presents a systematic treatment of Groebner bases, and more generally of the problem of normal forms, departing from linear algebra, going through commutative and noncommutative algebra, to operads. The algorithmic aspects are especially developed, with numerous examples and exercises. - Lo c Foissy By balancing computational methods and abstract reasoning, the authors of the book under review have written an excellent up-to-date introduction to Gr obner basis methods applicable to associative structures, especially including operads. The book will be of interest to a wide range of readers, from undergraduates to experts in the field. ~ Ralf Holtkamp, Mathematical Reviews, March 2018 This book presents a systematic treatment of Grobner bases, and more generally of the problem of normal forms, departing from linear algebra, going through commutative and noncommutative algebra, to operads. The algorithmic aspects are especially developed, with numerous examples and exercises. - Lo c Foissy Author InformationMurray 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. Vladimir Dotsenko, PhD, is an assistant professor in pure mathematics at Trinity College Dublin in Ireland. He studied at the Mathematical High School 57 in Moscow, Independent University of Moscow, and Moscow State University. His PhD thesis is titled Analogues of Orlik–Solomon Algebras and Related Operads. Dr. Dotsenko also held shorter positions at Dublin Institute for Advanced Studies and the University of Luxembourg. His collaboration with Murray started in February 2013 in CIMAT (Guanajuato, Mexico), where they both lectured in the research school ""Associative and Nonassociative Algebras and Dialgebras: Theory and Algorithms."" His primary research interests are algebraic operads, homotopical algebra, combinatorics, and representation theory. Tab Content 6Author Website:Countries AvailableAll regions |
||||
