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Free Lie Algebras : LONDON MATHEMATICAL SOCIETY MONOGRAPHS NEW SERIES - Christophe Reutenauer

Free Lie Algebras

LONDON MATHEMATICAL SOCIETY MONOGRAPHS NEW SERIES

Hardcover

Published: 6th May 1993
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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.

`...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

Introduction 1: Free Lie algebras 2: Lie polynomials 3: Algebraic properties 4: Logarithms and exponentials 5: Hall bases 6: Applications of Hall sets 7: Shuffle algebra and subwords 8: Circular words 9: the action of the symmetric group 10: The Solomon descent algebra References Index

ISBN: 9780198536796
ISBN-10: 0198536798
Series: LONDON MATHEMATICAL SOCIETY MONOGRAPHS NEW SERIES
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 286
Published: 6th May 1993
Publisher: Oxford University Press
Country of Publication: GB
Dimensions (cm): 24.77 x 16.51  x 2.54
Weight (kg): 0.62