Free Lie Algebras

Name: Free Lie Algebras
Price: 237.7 USD
Availability: InStock
ISBN: 9780198536796

ISBN-10: 0198536798

ISBN-13: 9780198536796

Edition: 1993

Authors: Christophe Reutenauer

List price: $295.00

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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,…

Book details

List price: $295.00
Copyright year: 1993
Publisher: Oxford University Press, Incorporated
Publication date: 6/10/1993
Binding: Hardcover
Pages: 286
Size: 6.14" wide x 9.21" long x 0.79" tall
Weight: 1.364
Language: English



Index of notation



Introduction



The Poincare-Birkhoff-Witt theorem



Free Lie algebras



Elimination



The polynomials



Words, polynomials, and series



Lie polynomials



Characterizations of Lie polynomials



Shuffles



Duality concatenation/shuffle



Algebraic properties



The weak algorithm



Subalgebras



Automorphisms



Free sets of Lie polynomials



Logarithms and exponentials



Lie series and logarithm



The canonical projections



Coefficients of the Hausdorff series



Derivation and exponentiation



Hail bases



Hall trees and words



Hall and Poincare-Birkhoff-Witt bases



Hall sets and Lazard sets



Applications of Hall sets



Lyndon words and basis



The dual basis



The derived series



Order properties of Hall sets



Synchronous codes



Shuffle algebra and subwords



The free generating set of Lyndon words



Presentation of the shuffle algebra



Subword functions



The lower central series of the free group



Circular words



The number of primitive necklaces



Hall words and primitive necklaces



Generation of Lyndon words



Factorization into Lyndon words



Words and multisets of primitive necklaces



The action of the symmetric group



Action of the symmetric group and of the linear group



The character of the free Lie algebra



Irreducible components



Lie idempotents



Representations on the canonical decomposition



The Solomon descent algebra



The descent algebra



Idempotents



Homomorphisms



Quasisymmetric functions and enumeration of permutations


References


Index