Free Lie Algebras (London Mathematical Society Monographs, 7) by Christophe Reutenauer (PDF)

Description

This much-needed new book is the first to specifically detail free Lie algebras. Lie polynomials appeared at the turn of the century and were identified with the free Lie algebra by Magnus and Witt some thirty years later. Many recent, important developments have occurred in the field–especially from the point of view of representation theory–that have necessitated a thorough treatment of the subject. This timely book covers all aspects of the field, including characterization of Lie polynomials and Lie series, subalgebras and automorphisms, canonical projections, Hall bases, shuffles and subwords, circular words, Lie representations of the symmetric group, related symmetric functions, descent algebra, and quasisymmetric functions. With its emphasis on the algebraic and combinatorial point of view as well as representation theory, this book will be welcomed by students and researchers in mathematics and theoretical computer science.

User’s Reviews

Editorial Reviews: Review `…expertly composed and skilfully organized. A book which involves a wealth of intricate and brand new lines of development should not be expected to be read easily, despite all conceptual clearness and lucidity of style. In this review, only a very small selection of exemplarily chosen results have been mentioned. The list of references consists of 233 items. The earliest are from the very first days of the theory, but almost exactly one quarter of them stem from the years 1989-1993. This fact, too, although a formal one, gives emphasis to the importance and timeliness of this publication.’ Hartmut Laue, Mathematical Reviews, Issue 94j About the Author Christophe Reutenauer is at Universite du Quebec a Montreal.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐With free Lie algebras becoming increasingly important in topology and computer science, this book is an invaluable resource. It is the only book on the market today which collects together the essential facts about free Lie algebras, which were previously widely scattered across numerous journals and known only to experts, and presents them in an accessible manner. This book works its way up from the fundamentals to what was known around 1993, which provides a strong basis for current research in the subject.

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