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Humphreys J.E. — Introduction To Lie Algebras And Representation Theory
Humphreys J.E. — Introduction To Lie Algebras And Representation Theory

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Название: Introduction To Lie Algebras And Representation Theory

Автор: Humphreys J.E.

Аннотация:

This book is designed to introduce the reader to the theory of semisimple Lie algebras over an algebraically closed field of characteristic 0, with emphasis on representations. A good knowledge of linear algebra (including eigenvalues, bilinear forms, Euclidean spaces, and tensor products of vector spaces) is presupposed, as well as some acquaintance with the methods of abstract algebra. The first four chapters might well be read by a bright undergraduate; however, the remaining three chapters are more demanding.

This text grew out of lectures which the author gave at the N.S.F. Advanced Science Seminar on Algebraic Groups at Bowdoin College in 1968.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Third Printing, revised

Год издания: 1972

Количество страниц: 171

Добавлена в каталог: 29.11.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$A_\ell$      2
$B(\Delta)$      84
$B_\ell$      3
$ch_{V}$      124
$ch_{\lambda}$      124
$C_\ell$      2
$C_{l}$      118
$C_{L}(X)$      7
$c_{\alpha\beta}$      145
$c_{\phi}$      27
$deg(\lambda)$      139
$Der\mathfrak{A}$      4
$D_\ell$      3
$e(\lambda)$      124
$E_{6}$, $E_{7}$, $E_{8}$      58
$f\textbulletg$      135
$F_{4}$      58
$G_{2}$      44
$G_{V}(K)$      162
$ht \alpha$      47
$H_{\alpha}$      37
$I(\lambda)$      110
$L^{(i)}$      10
$L^{i}$      11
$L_{a}(ad x)$      78
$L_{V}$      159
$L_{V}(K)$      162
$m(\mu)$      118
$M_{max}$      162
$M_{min}$      161
$m_{\lambda}(\mu)$      117
$N(\delta)$      84
$n(\sigma)$      51
$N_{L}(K)$      7
$p(\lambda)$      135
$P_{\alpha}$      42
$q(\lambda)$      136
$sn(\sigma)$      54 136
$S_{\alpha}$      38
$T_{\alpha}$      37
$V(\lambda)$      110
$V_{\lambda}$      107
$Y(\lambda)$      110
$Z(\lambda)$      110
$Z[\Lambda]$      124
$\alpha$-string through $\beta$      39 45
$\alpha$-string through $\mu$      114
$\alpha^{V}$      43
$\chi_{\lambda}$      129
$\Delta$      47
$\Delta(\gamma)$      48
$\ell(\sigma)$      51
$\gamma$      65
$\Gamma(L)$      77 87
$\kappa(x,y)$      21
$\lambda$      67 112
$\lambda\sim\mu$      129
$\Lambda^{+}$      67 112
$\lambda_{i}$      67
$\Lambda_{r}$      67
$\langle\alpha,\beta\rangle$      42
$\mathfrak{C}$      104
$\mathfrak{C}(\Delta)$      49
$\mathfrak{C}(\gamma)$      49
$\mathfrak{C}_{0}$      105
$\mathfrak{d}(n, F)$      3
$\mathfrak{gl}(n, F)$      2
$\mathfrak{gl}(V)$      2
$\mathfrak{M}_{\lambda}$      137
$\mathfrak{n}(n, F)$      3
$\mathfrak{o}(n, F)$      3
$\mathfrak{o}(V)$      3
$\mathfrak{P}(H)\mathscr{W}$      127
$\mathfrak{P}(L)^{G}$      127
$\mathfrak{P}(V)$      126
$\mathfrak{sl}(n, F)$      2
$\mathfrak{sl}(V)$      2
$\mathfrak{sp}(n, F)$      3
$\mathfrak{sp}(V)$      3
$\mathfrak{S}(V)$      89
$\mathfrak{t}(n, F)$      3
$\mathfrak{T}(V)$      89
$\mathfrak{U}(L)$      91
$\mathfrak{U}(L)_{Z}$      156
$\mathfrak{X}$      135
$\mathfrak{Z}$      128
$\mathscr{E}(L)$      82
$\mathscr{E}(L;K)$      82
$\mathscr{N}(L)$      82
$\mathscr{R}$      133
$\mathscr{S}_{m}$      90
$\mathscr{W}$      43
$\Phi$      35 42
$\Phi^{+}$      47
$\Phi^{-}$      47
$\Phi^{v}$      43
$\Pi(V)$      113
$\Pi(\lambda)$      113
$\sigma_{\alpha}$      42
$\succ$      47
$\theta(\lambda)$      137
$\tilde{\mathfrak{S}}(V)$      90
$\varepsilon_{\lambda}$      135
Abelian Lie algebra      4
Abstract Jordan decomposition      24
Ad-nilpotent      12
Ad-semisimple      24
Adjoint Chevalley group      150
Adjoint representation      4
Admissible lattice      159
Affine n-space      132
Algebra      4
Associative bilinear form      21
Automorphism      8
Base of root system      47
Borel subalgebra      83
Bracket      1 2
Canonical map      7
Cartan decomposition      35
Cartan integer      39 55
Cartan matrix      55
Cartan subalgebra (CSA)      80
Cartan’s criterion      20
Casimir element      27 118
Cayley algebra      104
Center (of Lie algebra)      6
Center (of universal enveloping algebra)      128
centralizer      7
CHARACTER      129
Character (formal)      124
Chevalley algebra      149
Chevalley basis      147
Chevalley group      150 163
Chevalley’s theorem      127
Classical Lie algebra      2
Clebsch — Gordan formula      126
Closed set of roots      87 154
Commutator      1
Completely reducible module      25
Contragredient module      26
Convolution      135
Coxeter graph      56
CSA      80
Degree      139
Derivation      4
Derived algebra      6
Derived series      10
Descending central series      11
Diagonal automorphism      87
Diagonal matrices      3
Diagram automorphism      66
Direct sum of Lie algebras      22
Dominant integral linear function      112
Dominant weight      67
Dual module      26
Dual root system      43
Dynkin diagram      57
e      40 42
End V      2
Engel subalgebra      79
Engel’s theorem      12
Epimorphism      7
Equivalent representations      25
Exceptional Lie algebras      102
Faithful representation      27
Flag      13
Formal character      124
Free Lie algebra      94
Freudenthal’s formula      122
Fundamental domain      52
Fundamental dominant weight      67
Fundamental group      68
Fundamental Weyl chamber      49
g(k)      150
General linear algebra      2
General linear group      2
Generators and relations      95
GL(V)      2
Graph automorphism      66 87
Group ring      124
H(Z)      159
Harish-Chandra’s Theorem      130
Height      47
Highest weight      32 70 108
Homogeneous symmetric tensor      90
Homomorphism (of L-modules)      25
Homomorphism (of Lie algebras)      7
Hyperplane      42
Ideal      6
Induced module      109
Inner automorphism      9
Inner derivation      4
Int L      9
Integral linear function      112
Invariant polynomial function      126
Inverse root system      43
Irreducible module      25
Irreducible root system      52
Irreducible set      133
Isomorphism (of L-modules)      25
Isomorphism (of Lie algebras)      1
Isomorphism (of root systems)      43
Jacobi identity      1
Jordan — Chevalley decomposition      17
Killing form      21
Kostant function      136
Kostant’s formula      138
Kostant’s Theorem      156
L(K)      149
L(Z)      149
Lattice      64 157
Length (in Weyl group)      51
Lie algebra      1
Lie’s theorem      16
Linear lie algebra      2
Linked weights      129
Locally nilpotent      99
Long root      53
Lower central series      11
Maximal toral subalgebra      35
Maximal vector      32 108
Minimal weight      72
Module (for Lie algebra)      25
Monomorphism      7
Multiplicity of weight      117
Negative root      47
Nilpotent endomorphism      8
Nilpotent Lie algebra      11
Nilpotent part      17 24
Non-reduced root system      66
Nondegenerate bilinear form      22
normalizer      7
Octonion algebra      104
Orthogonal algebra      3
Orthogonal matrix      10
Outer derivation      4
Parabolic subalgebra      88
Partition function      136
PBW      92
PBW basis      92
Poincare — Birkhoff — Witt theorem      92
Polynomial function      126 133
Positive root      47
Quotient Lie algebra      7
Rad L      11
Radical (of bilinear form)      22
Radical (of Lie algebra)      11
Rank (of Lie algebra)      86
Rank (of root system)      43
Reduced      51
Reductive Lie algebra      30 102
Reflecting hyperplane      42
Reflection      42
Regular      48
Regular semisimple element      80
Representation      8
Root      35
Root lattice      67
Root space decomposition      35
Root system      42
Saturated set of weights      70
Scalar matrices      5
Schur’s lemma      26
Self-normalizing subalgebra      7
Semisimple endomorphism      17
Semisimple Lie algebra      11
Semisimple part      17 24
Serre’s theorem      99
Short root      53
Simple Lie algebra      6
Simple reflection      51
Simple root      47
singular      48
Skew-symmetric tensor      117
SL(V)      2
Solvable Lie algebra      10
Special linear algebra      2
Special linear group      2
Standard Borel subalgebra      84
Standard cyclic module      108
Standard parabolic subalgebra      88
Standard set of generators      74
Steinberg’s Formula      141
Strictly upper triangular matrices      3
Strongly ad-nilpotent      82
Strongly dominant weight      67
Structure constants      4
Subalgebra (of Lie algebra)      1
Support      135
Symmetric algebra      89
Symmetric tensor      90
Symplectic algebra      3
Tensor algebra      89
Tensor product of modules      26
Toral subalgebra      35
tr      2
Trace      2
Trace polynomial      128
Universal Casimir element      118
Universal Chevalley group      161
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