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Reutenauer Ch. — Free Lie Algebras
Reutenauer Ch. — Free Lie Algebras

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Название: Free Lie Algebras

Автор: Reutenauer Ch.

Аннотация:

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.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1993

Количество страниц: 286

Добавлена в каталог: 09.04.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
A-adic topology      17
Admissible pyramid      170
Algebra of divided powers      108
Algebra of functions on the free group      132
Alphabet      14
Alphabetical order      105
Antipode      29
Antisymmetry      1
Baker’s identity      36
Bernoulli numbers      72
Bialgebra      27
Bilinear system      149
Binomial coefficient      131
Bisection      126
Campbell — Baker — Hausdorff formula      56
Canonical projections      59
Cardinality of a multiset      166
Causal analytic functional      148
Characteristic      178
Chen series      80
Circular word      154
Closed      11
Code      119
Column sum      218
Comma-free      122
Compatible      227
complete      119
Complete symmetric function      202
Complete tensor product      28
composition      218
Concatenation algebra      15
Concatenation product      14 15
Confluent      86
Conjugacy class      154 170
Conjugate words      154
Conjugation      154 170
Constant term      17
Convolution product      28
Cycle type      178
Cyclic language      160
Cyclically standard      174
Decreasing factorization into Hall words      89
Decreasing sequence      86 137
Defect theorem      49
Degree      5 16
Dependent      40
Derivation      7 19 36 76
Derivation tree      91
Derived ideal      49
Derived series      112
Descent      62 185
Descent composition      222
Descent set      62 185
Differentia] polynomial      149
Dual coalgebra      38
Dynkins formula      81
Elementary automorphims      47
Empty word      14
Enveloping algebra      2
Eulerian polynomial      62 63
Evaluation      156 166
Exponent of a word      154
Exponential      54
Factor      14
Factorization of the free monoid      173
Finely homogeneous component      16
Finely homogeneous polynomial      16
Finer      227
Finite Lie rank      149
foliage      84
Formal series      17
Free associative algebra      6 15
Free Lie algebra      4
Free Lie p-algebra      35
Free Lie superalgebra      102
Free magma      4
Free monoid      14
Free partially commutative Lie algebra      102
Free partially commutative monoid      101
Free set of Lie polynomials      49
Frobenius image      178
Generating function      156 179
Graded bialgebra      248
Grobner formula      148
Hall polynomial      90
Hall set      84 89
Hall tree      85
Hall word      89
Hausdorff series      56
Highest homogeneous component      43
Homogeneous component      16
Homogeneous endomorphism      30 177
Homogeneous eulerian polynomial      63
Homogeneous polynomial      16
Hopf algebra      29
Immediate subtree      84
Infiltration      135
Infiltration product      134
Inner product of symmetric functions      233
inversion      86 137
Invertible      86
Iterated integral      56 148
Jacobi identity      1
Jacobian conjecture      51
Jacobian matrix      46 47
Jacobson formulas      33
Labelled standard sequence      143
Language      38
Lazard set      11
Left action      176
Left comb      212
Left factor      14
Left unitary      119
Legal rise      86 137
Length      14 166 218
letter      14
Level      113
Lie algebra      1
Lie bracket      1
Lie dependent      42
Lie endomorphism      30
Lie idempotent      194
Lie invariant      207
Lie monomial      236
Lie polynomial      18
Lie product      1
Lie representation      180
Lie series      52
Locally finite      18
Logarithm      54
Lower central series      136
Lyndon element      170
Lyndon word      105
Magma      4
Magnus transformation      132
Major index      185
Message      122
Moebius function      150
Multilinear part      178 180
Multiliner polynomial      125
Multiplicity in a multiset      166
Multiset      166
Necklace      154
Noncommutative polynomial      15
Nontrivial factor      14
Nontrivial sesquipower      164
Normal basis      171
Order associated to a Hall set      114
Palindrome      33
Partial degree      16
Period of a necklace, a word      154
Periodic expansion of a word      161
Plethysm      202
Polynomial      15
Power sum      156 178
Prefix      14
Primitive element      35 170
Primitive necklace, word      154
Product of functions on the free group      132
Proper factor      14
Proper homomorphism      46
Pseudocomposition      218
Pseudocomposition associated to a matrix      218
Pyramid      170
Quasi-symmetric function      242
Quasi-symmetric generating function      245
Rank of a free Lie algebra      50
Rational series      38
Recognizable function      133
Recognizable series      38
Recognizable subset      150
Representative function      133
Representative subset      150
Restricted enveloping algebra      50
Restricted Lie algebra of characteristic p      50
Reversal      28
Right action      177
Right factor      14
Rise      62 86 137
Rise set      62
Row sum      218
Schur function      186
Semi-direct product      8
Series      17
Sesquipower      164
Shift mapping      168
Shuffle      24
Shuffle algebra      24
Shuffle product      24
SIZE      73
Space of subword functions      132
Standard factorization      89 170
Standard list      126
Standard numbering      166
Standard permutation      167
Standard sequence      85 136
Standard tableau      185
Substitution of letters      30
Subword      23 131
Subword function      131 132
Subword order      150
Suffix      14
Suffix code      119
Support of the free Lie algebra      33
Symmetrized product      57
synchronizing      119
TREE      4
TYPE      227
Weight      218 224 227
Weight-preserving      231
Word      14
Young subgroup      249
Zassenhaus formula      81
Zeta function      174
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