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Milnor J., Husemoller D. — Symmetric Bilinear Forms
Milnor J., Husemoller D. — Symmetric Bilinear Forms



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Название: Symmetric Bilinear Forms

Авторы: Milnor J., Husemoller D.

Аннотация:

The theory of quadratic forms and the intimately related theory of symmetric bilinear forms have a long and rich history, highlighted by the work of Legendre, Gauss, Minkowski, and Hasse. (Compare [Dickson] and [Bourbaki, 24, p. 185].) Our exposition will concentrate on the relatively recent developments which begin with and are inspired by Witt's 1937 paper "Theorie der quadratischen Formen in beliebigen Korpern." We will be particularly interested in the work of A. Pfister and M. Knebusch. However, some older material will be described, particularly in ChapterII. The presentation is based on lectures by Milnor at the Institute for Advanced Study, and at Haverford College under the Phillips Lecture Program, during the Fall of 1970, as well as lectures at Princeton University in 1966


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1973

Количество страниц: 146

Добавлена в каталог: 18.11.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$B^{t}$ (transpose of matrix)      3
$E_{6},E_{7},E_{8}$ (root systems)      28 31 139
$I_{n}$(genus of $n\langle1\rangle$)      46 49
$M^{\bot}$ (orthogonal complement)      5
$R^{\bullet}$ (units of ring)      4
$\Gamma_{8}$ (lattice)      27—29 31 35 44 47 103 139
$\langle B\rangle$, $\langle u\rangle$ (inner product space specified by matrix)      3 4
$\mathds{Q},\mathds{Q_{p}}$      20
$\mathds{Z}$, $\mathds{Z}_{p}$, $\mathds{Z}_{\infty}$      15 42 43
$\mathds{Z}^{\Omega}$      63 64
$\omega_{n}$ (volume)      16 31
Anisotropic space      56 112
Arason, J.K.      76
Arf, Cahit      112
Artin — Schreier theorem      60
Asymptotic estimates      17 31 35 50
Bachet de Meziriac      40
Bilinear form      1
Bilinear form module or space      2
Blichfeldt, H.F.      29 35
Braun, Hel      127 130
Characteristic two      56 82 100 112
Convex set      16
Convolution      55
Conway, J.H.      28 46
Cyclic Witt groups      23 66 69 87 99
Dedekind domains      7 91 93
Density $Df^{-1}$ of solutions      42
Density of packing      34
Determinant      4 12 16 115 119
Dirichlet, P.G.L.      98 129
Discrete valuation      84
Discriminant d of a Witt class      77
Discriminant of a field extension      107
Dual basis      4
Dual lattice $L^{\#}$      25 26 48 91 127
Dyadic prime      94
Dynkin diagram      139
Eichler, Martin      27
Eisenstein, Gotthold      18 45
Euler, Leonhard      39
Exterior power      12 107
Extreme lattice or matrix      29 38
Face centered cubic lattice      30 31 35
Fermat, Pierre de      39
Finite field $F_{q}$      21 81 87 117
Fourier series      129
Fundamental domain      15
Fundamental ideal I      66
Gauss sums      51 127
Gaussian integers      39 95
Genus of symmetric bilinear form      43
Global field      120
Hasse invariant H      79
Hasse norm theorem      121
Hasse — Minkowski theorem      20 89 120
Hasse — Witt invariant h      80
Hermite, Charles      18
Hermitian form      114
Hilbert symbol      78 134
Hlawka, E.      32 46
Hyperbolic plane      9 12—13 101
I (fundamental ideal)      66
Ideal class group      93 95
Idele group      124
Indecomposable lattice      27
Indefinite bilinear form      21
Index of isotropy      57
Inertia theorem      23 61
Inner product      1
Inner product module or space      2
Integers $\mathds{Z}$      15 90
Integers of number field      94 107
Intersection number      100
Involution      114
Jacob son, Nathan      115 118
Jacobi, C.G.J.      23 45 61
Klein bottle      101
Knebusch, Manfred      12 14 85 95 127 131
Kneser, Martin      28
Korkine, Alexander ( = Korkin, Aleksandr)      28 29 38146
Lagrange, Joseph Louis      40
Lattice      15 91
Leech, John      28 35 135
Legendre symbol      43 51 132
Leicht, J.      65
Level s of a field      75
Local ring      6—8 14 68 86
Lorenz, Falko      65
Lusztig, g.      106
Mass (of genus)      49
Mathieu group      137
Meyer, Arnold      20
Milgram, James      25 127
Minimal vector      27
Minkowski, Hermann      16 20 31 41
Multiplicative inner product space      72
Niemeier, H.-V.      138
Nilpotent elements, nilradical      68 69 76
Norm (in various senses)      23 72 115 121
Number field      61 64 81 94 107 118
Ordering of field      59 67
Orientation      94 101 103
Orthogonal      2
Orthogonal sum, complement, basis      4—6
p-adic integers $\mathds{Z_{p}}$      21 25 42
p-adic numbers $\mathds{Q_{p}}$      20 81 89
Packing of euclidean space      34
Pfaffian      7
Pfister, A.      65 72 76
Positive definite      16 26 61
Projective module      2
Projective plane      101 103
Pythagorean field      71
Quadratic form      22 110
Quadratic inner product space      111
Quadratic reciprocity      132—134
Quaternion algebra      118
Radical      68 69 95
Radon — Nikodym theorem      42
Rank      3 11
Rational numbers $\mathds{Q}$      20 87
Real fields, real closure      60 71
Reflection      7 138
Regular hexagonal lattice      30 35
Represent      120 124
Residue class field      84
Residue class form      85
Rogers, C.A.      31 35
Root systems      31 138
Scharlau, Winfried      71 133
Self—dual lattice      46 91
Shoe box principle      21
Siegel, Carl Ludwig      44—49
Signature $\sigma$      23—25 62—64 69 127
Similarity transformation      29 76
Simple finite groups      28 137
Skew bilinear form      2
Smith, H.J.S.      28 41
Split inner product space      12
Springer, T.A.      85
Square theorem      124
Steinberg, Robert      47 78 81
Steinitz, Ernst      7 107
Stirling's formula      31
Sums of squares      39 41 45 74
Sylvester, J.J.      23 61
Symbol      78
Symmetric bilinear form      2
Symplectic basis      7 106
Symplectic bilinear form      2 7 105
Tensor product      10 47 73 111
Thompson, John      46
Thue, A.      35
Torsion in Witt ring      68 69 72
Torus      16 101
Totally positive      61 95
Totally real, imaginary      95
Type I, type II      22—25
Unimodular lattice      16
Valuation, valuation ring      84
van der Blij, F.      24 25
Vector bundles      105—107
Volume      15 34 42
Voronoi polyhedron      30
Weak approximation theorem      123
Weil, Andre      131—134
Witt ring of $\mathds{Z}$      23 90
Witt ring, Witt class      14 112 114
Witt rings of special fields      81 87 88
Witt, Ernst      8 28 84 137
Zolotareff, G. (= Zolotarev, E.I.)      28 38
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