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1.

図書

図書
Franz Georg Timmesfeld
出版情報: Basel ; Boston : Birkhäuser Verlag, c2001  xiii, 389 p. ; 24 cm
シリーズ名: Monographs in mathematics ; v. 95
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2.

図書

図書
G. Lusztig
出版情報: Providence, R.I. : American Mathematical Society, c2003  vi, 136 p. ; 26 cm
シリーズ名: CRM monograph series ; v. 18
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3.

図書

図書
Patrice Tauvel, Rupert W. T. Yu
出版情報: Berlin : Springer, c2005  xvi, 653 p. ; 25 cm
シリーズ名: Springer monographs in mathematics
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目次情報: 続きを見る
Preface
Results on topological spaces / 1:
Irreducible sets and spaces / 1.1:
Dimension / 1.2:
Noetherian spaces / 1.3:
Constructible sets / 1.4:
Gluing topological spaces / 1.5:
Rings and modules / 2:
Ideals / 2.1:
Prime and maximal ideals / 2.2:
Rings of fractions and localization / 2.3:
Localization of modules / 2.4:
Radical of an ideal / 2.5:
Local rings / 2.6:
Noetherian rings and modules / 2.7:
Derivations / 2.8:
Module of differentials / 2.9:
Integral extensions / 3:
Integral dependence / 3.1:
Integrally closed rings / 3.2:
Extensions of prime ideals / 3.3:
Factorial rings / 4:
Generalities / 4.1:
Unique factorization / 4.2:
Principal ideal domains and Euclidean domains / 4.3:
Polynomial and factorial rings / 4.4:
Symmetric polynomials / 4.5:
Resultant and discriminant / 4.6:
Field extensions / 5:
Extensions / 5.1:
Algebraic and transcendental elements / 5.2:
Algebraic extensions / 5.3:
Transcendence basis / 5.4:
Norm and trace / 5.5:
Theorem of the primitive element / 5.6:
Going Down Theorem / 5.7:
Fields and derivations / 5.8:
Conductor / 5.9:
Finitely generated algebras / 6:
Noether''s Normalization Theorem / 6.1:
Krull''s Principal Ideal Theorem / 6.3:
Maximal ideals / 6.4:
Zariski topology / 6.5:
Gradings and filtrations / 7:
Graded rings and graded modules / 7.1:
Graded submodules / 7.2:
Applications / 7.3:
Filtrations / 7.4:
Grading associated to a filtration / 7.5:
Inductive limits / 8:
Inductive systems of maps / 8.1:
Inductive systems of magmas, groups and rings / 8.3:
An example / 8.4:
Inductive systems of algebras / 8.5:
Sheaves of functions / 9:
Sheaves / 9.1:
Morphisms / 9.2:
Sheaf associated to a presheaf / 9.3:
Gluing / 9.4:
Ringed space / 9.5:
Jordan decomposition and some basic results on groups / 10:
Jordan decomposition / 10.1:
Generalities on groups / 10.2:
Commutators / 10.3:
Solvable groups / 10.4:
Nilpotent groups / 10.5:
Group actions / 10.6:
Generalities on representations / 10.7:
Examples / 10.8:
Algebraic sets / 11:
Affine algebraic sets / 11.1:
Regular functions / 11.2:
Examples of morphisms / 11.4:
Abstract algebraic sets / 11.6:
Principal open subsets / 11.7:
Products of algebraic sets / 11.8:
Prevarieties and varieties / 12:
Structure sheaf / 12.1:
Algebraic prevarieties / 12.2:
Morphisms of prevarieties / 12.3:
Products of prevarieties / 12.4:
Algebraic varieties / 12.5:
Rational functions / 12.6:
Local rings of a variety / 12.8:
Projective varieties / 13:
Projective spaces / 13.1:
Projective spaces and varieties / 13.2:
Cones and projective varieties / 13.3:
Complete varieties / 13.4:
Products / 13.5:
Grassmannian variety / 13.6:
Dimension of varieties / 14:
Dimension and the number of equations / 14.2:
System of parameters / 14.3:
Counterexamples / 14.4:
Morphisms and dimension / 15:
Criterion of affineness / 15.1:
Affine morphisms / 15.2:
Finite morphisms / 15.3:
Factorization and applications / 15.4:
Dimension of fibres of a morphism / 15.5:
Tangent spaces / 15.6:
A first approach / 16.1:
Zariski tangent space / 16.2:
Differential of a morphism / 16.3:
Some lemmas / 16.4:
Smooth points / 16.5:
Normal varieties / 17:
Normalization / 17.1:
Products of normal varieties / 17.3:
Properties of normal varieties / 17.4:
Root systems / 18:
Reflections / 18.1:
Root systems and bilinear forms / 18.2:
Passage to the field of real numbers / 18.4:
Relation between two roots / 18.5:
Base of a root system / 18.6:
Weyl chambers / 18.7:
Highest root / 18.8:
Closed subsets of roots / 18.9:
Weights / 18.10:
Graphs / 18.11:
Dynkin diagrams / 18.12:
Classification of root systems / 18.13:
Lie algebras / 19:
Generalities on Lie algebras / 19.1:
Representations / 19.2:
Nilpotent Lie algebras / 19.3:
Solvable Lie algebras / 19.4:
Radical and the largest nilpotent ideal / 19.5:
Nilpotent radical / 19.6:
Regular linear forms / 19.7:
Cartan subalgebras / 19.8:
Semisimple and reductive Lie algebras / 20:
Semisimple Lie algebras / 20.1:
Semisimplicity of representations / 20.2:
Semisimple and nilpotent elements / 20.4:
Reductive Lie algebras / 20.5:
Results on the structure of semisimple Lie algebras / 20.6:
Subalgebras of semisimple Lie algebras / 20.7:
Parabolic subalgebras / 20.8:
Algebraic groups / 21:
Subgroups and morphisms / 21.1:
Connectedness / 21.3:
Actions of an algebraic group / 21.4:
Modules / 21.5:
Group closure / 21.6:
Affine algebraic groups / 22:
Translations of functions / 22.1:
Jordan / 22.2:
Preface
Results on topological spaces / 1:
Irreducible sets and spaces / 1.1:
4.

図書

図書
T.A. Springer
出版情報: Boston : Birkhäuser, c1998  x, 334 p. ; 25 cm
シリーズ名: Progress in mathematics ; v. 9
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5.

図書

図書
Kevin P. Knudson
出版情報: Basel ; Boston : Birkhäuser Verlag, c2001  xi, 192 p. ; 24 cm
シリーズ名: Progress in mathematics ; v. 193
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6.

図書

図書
Michel Waldschmidt
出版情報: Berlin : Springer, c2000  xxiii, 633 p. ; 25 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; 326
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目次情報: 続きを見る
Introduction and Historical Survey / 1:
Linear Independence of Logarithms of Algebraic Numbers / Part I:
Transcendence Proofs in One Variable / 2:
Heights of Algebraic Numbers / 3:
The Criterion of Schneider-Lang / 4:
Zero Estimate / 5:
Measures of Linear Independence / 6:
A First Measure with a Simple Proof / 7:
Zero Estimate (Continued), by Damien ROY / 8:
Refined Measure / 9:
Multiplicities in Higher Dimension / III:
Multiplicity Estimates, by Damien ROY / 10:
Interpolation Determinants with One Derivative / 11:
On Baker's Method / 12:
The Linear Subgroup Theorem / Part IV:
Points Whose Coordinates are Logarithms of Algebraic Numbers / 13:
Lower Bounds for the Rank of Matrices / 14:
Simultaneous Approximation of Values of the Exponential Function in Several Variables / Part V:
A Quantitative Version of the Linear Subgroup Theorem / 15:
Applications to Diophantine Approximation / 16:
Algebraic Independence / 17:
References
Introduction and Historical Survey / 1:
Linear Independence of Logarithms of Algebraic Numbers / Part I:
Transcendence Proofs in One Variable / 2:
7.

図書

図書
Goro Shimura
出版情報: Providence, R.I. : American Mathematical Society, c2004  ix, 275 p. ; 27 cm
シリーズ名: Mathematical surveys and monographs ; v. 109
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8.

図書

図書
Meinolf Geck
出版情報: Oxford : Oxford University Press, 2003  xii, 307 p. ; 24 cm
シリーズ名: Oxford graduate texts in mathematics ; 10
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目次情報: 続きを見る
Algebraic sets and algebraic groups / 1:
Affine varieties and finite morphisms / 2:
Algebraic representations and Borel subgroups / 3:
Frobenius maps and finite groups of Lie type / 4:
Bibliography
Index
Algebraic sets and algebraic groups / 1:
Affine varieties and finite morphisms / 2:
Algebraic representations and Borel subgroups / 3:
9.

図書

図書
Jens Carsten Jantzen
出版情報: Boston ; Tokyo : Academic Press, c1987  xiii, 443 p. ; 24 cm
シリーズ名: Pure and applied mathematics ; v. 131
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10.

図書

図書
Jean-Pierre Serre ; translated from the French by John Stillwell
出版情報: Berlin ; New York : Springer-Verlag, 1980  ix, 142 p. ; 25 cm
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11.

図書

図書
A. Weil
出版情報: Boston : Birkhäuser, 1982  126 p. ; 24 cm
シリーズ名: Progress in mathematics ; vol. 23
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12.

図書

図書
T.A. Springer
出版情報: Boston : Birkhäuser, 1981  x, 304 p. ; 23 cm
シリーズ名: Progress in mathematics ; v. 9
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13.

図書

図書
Jean-Pierre Serre
出版情報: Paris : Hermann, c1959  202 p. ; 24 cm
シリーズ名: Publications de l'Institut de mathématique de l'Université de Nancago ; 7
Actualités scientifiques et industrielles ; 1264
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14.

図書

図書
Armand Borel ; notes taken by Hyman Bass
出版情報: New York : W.A. Benjamin, 1969  xi, 398 p. ; 24 cm
シリーズ名: Mathematics lecture note series
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15.

図書

図書
Jean-Pierre Serre
出版情報: New York ; Tokyo : Springer-Verlag, c1988  ix, 207 p. ; 25 cm
シリーズ名: Graduate texts in mathematics ; 117
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目次情報: 続きを見る
Summary of the Main Results
Algebraic Curves
Maps From a Curve to a Commutative Group
Singular Algebraic Curves
Generalized Jacobians
Class Field Theory
Group Extension and Cohomology
Bibliography
Supplementary Bibliography
Index
Summary of the Main Results
Algebraic Curves
Maps From a Curve to a Commutative Group
16.

図書

図書
Walter Benz
出版情報: Berlin ; New York : Springer-Verlag, 1973  vii, 368 p. ; 24 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; Bd. 197
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17.

図書

図書
Karel Dekimpe
出版情報: Berlin : Springer, c1996  x, 259 p. ; 24 cm
シリーズ名: Lecture notes in mathematics ; 1639
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18.

図書

図書
James E. Humphreys
出版情報: Providence, R.I. : American Mathematical Society, c1995  xviii, 196 p. ; 26 cm
シリーズ名: Mathematical surveys and monographs ; v. 43
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目次情報: 続きを見る
Review of semisimple groups
Basic facts about classes and centralizers
Centralizers of semisimple elements
The adjoint quotient Regular elements
Parabolic subgroups and unipotent classes
The unipotent variety and the flag variety
Nilpotent orbits and unipotent classes
Finite groups of Lie type
Springer's Weyl group representations Complements
References
Index
Review of semisimple groups
Basic facts about classes and centralizers
Centralizers of semisimple elements
19.

図書

図書
A.N. Parshin, I.R. Shafarevich (eds.)
出版情報: Berlin ; Tokyo : Springer-Verlag, c1994  284 p. ; 25 cm
シリーズ名: Encyclopaedia of mathematical sciences / editor-in-chief, R.V. Gamkrelidze ; v. 55 . Algebraic geometry ; 4
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目次情報:
Linear Algebraic Groups / T.A. Springer
Invariant Theory / V.L. Popov ; E.B. Vinberg
Linear Algebraic Groups / T.A. Springer
Invariant Theory / V.L. Popov ; E.B. Vinberg
20.

図書

図書
A.I. Kostrikin, I.R. Shafarevich (eds.)
出版情報: Berlin ; New York : Springer-Verlag, c1993  203 p. ; 24 cm
シリーズ名: Encyclopaedia of mathematical sciences / editor-in-chief, R.V. Gamkrelidze ; v. 37 . Algebra ; 4
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21.

図書

図書
Gerhard P. Hochschild
出版情報: New York : Springer-Verlag, c1981  viii, 267 p. ; 24 cm
シリーズ名: Graduate texts in mathematics ; 75
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22.

図書

図書
Irving Reiner ; edited by Gerald J. Janusz
出版情報: Urbana : University of Illinois Press, c1989  xxvi, 785 p. ; 27 cm
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23.

図書

図書
E.R. Kolchin
出版情報: New York : Academic Press, 1973  xvii, 446 p. ; 24 cm
シリーズ名: Pure and applied mathematics ; v. 54
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24.

図書

図書
T.A. Springer
出版情報: Berlin ; New York : Springer-Verlag, 1973  vi, 168 p. ; 24 cm
シリーズ名: Ergebnisse der Mathematik und ihrer Grenzgebiete ; Bd. 75
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25.

図書

図書
[par] Michel Demazure, Pierre Gabriel ; avec un appendice, Corps de classes local, par Michel Hazewinkel
出版情報: Paris : Masson , Amsterdam : North-Holland, 1970  xxvi, 700 p. ; 23 cm
シリーズ名: Groupes algébriques ; t. 1
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26.

図書

図書
[par] Jean A. Dieudonné
出版情報: Berlin ; New York : Springer-Verlag, 1971  viii, 129 p. ; 24 cm
シリーズ名: Ergebnisse der Mathematik und ihrer Grenzgebiete ; Bd. 5
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27.

図書

図書
Armand Borel
出版情報: New York ; Tokyo : Springer-Verlag, c1991  x, 288 p. ; 25 cm
シリーズ名: Graduate texts in mathematics ; 126
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目次情報: 続きを見る
Background Material from Algebraic Geometry
General Notions Associated with Algebraic Groups
Homogeneous Spaces
Solvable Groups
Borel Subgroups; Reductive Groups
Rationality Questions
References
Index of Definition
Index of Notation
Background Material from Algebraic Geometry
General Notions Associated with Algebraic Groups
Homogeneous Spaces
28.

図書

図書
Séminaire C. Chevalley (1956-1958 : Paris, France) ; Chevalley, C. (Claude), 1909- ; École normale supérieure (France)
出版情報: Paris : Secrétariat mathématique, 1958  2 v. ; 27 cm
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29.

図書

図書
Robert Bédard
出版情報: Montréal : Centre de recherches mathématiques, 1991  149 p. ; 25 cm
シリーズ名: Les publications CRM ; . Notes de cours
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30.

図書

図書
par Jean Dieudonné
出版情報: Berlin : Springer, 1963  viii, 125 p. ; 24 cm
シリーズ名: Ergebnisse der Mathematik und ihrer Grenzgebiete ; Neue Folge, Bd. 5, Reihe : Gruppentheorie
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31.

図書

図書
Roe Goodman, Nolan R. Wallach
出版情報: Cambridge : Cambridge University Press, 1998  xvi, 685 p. ; 25 cm
シリーズ名: Encyclopedia of mathematics and its applications / edited by G.-C. Rota ; v. 68
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目次情報: 続きを見る
Classical groups as linear algebraic groups / 1:
Basic structure of classical groups / 2:
Algebras and representations / 3:
Polynomials and tensor invariants / 4:
Highest weight theory / 5:
Spinors / 6:
Cohomology and characters / 7:
Branching laws / 8:
Tensor representations of GL(V) / 9:
Tensor represenations of O(V) and Sp(V) / 10:
Algebraic groups and homogeneous spaces / 11:
Representations on Aff(X) / 12:
Algebraic geometry / A:
Linear and multilinear algebra / B:
Associative algebras and Lie algebras / C:
Manifolds and Lie groups / D:
Classical groups as linear algebraic groups / 1:
Basic structure of classical groups / 2:
Algebras and representations / 3:
32.

図書

図書
Max-Albert Knus ... [et al.] ; with a preface by J. Tits
出版情報: Providence, R.I. : American Mathematical Society, c1998  xxi, 593 p. ; 26 cm
シリーズ名: Colloquium publications / American Mathematical Society ; v. 44
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33.

図書

図書
V.E. Voskresenskiĭ ; [translated from the original Russian manuscript by Boris Kunyavski]
出版情報: Providence, R.I. : American Mathematical Society, c1998  xiii, 218 p. ; 26 cm
シリーズ名: Translations of mathematical monographs ; v. 179
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34.

図書

図書
Alexander J. Hahn, O. Timothy O'Meara ; foreword by J. Dieudonné
出版情報: Berlin ; Tokyo : Springer-Verlag, c1989  xv, 576 p. ; 24 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; 291
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35.

図書

図書
Armand Borel
出版情報: Paris : Hermann, c1969  124 p. ; 24 cm
シリーズ名: Actualités scientifiques et industrielles ; 1341
Publications de l'Institut de Mathématique de l'Université de Strasbourg ; 15
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