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1.

図書

図書
Wilhelm Killing ; herausgegeben von Wolfgang Hein
出版情報: Braunschweig : Deutsche Mathematiker-Vereinigung, c1997  v, 247 p. ; 23 cm
シリーズ名: Dokumente zur Geschichte der Mathematik ; Bd. 9
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2.

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:
3.

図書

図書
Willem A. de Graaf
出版情報: Amsterdam : Elsevier, 2000  xii, 393 p. ; 23 cm
シリーズ名: North-Holland mathematical library ; v. 56
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Basic constructions
On nilpotency and colvability
Cartan subalgebras
Lie algebras with non-degenerate Killing form
The classification of the simple Lie algebras
Universal enveloping algebras
Finitely presented Lie algebras
Representations of semisimple Lie algebras
On associative algebras
Bibliography
Index of Symbols
Index of Terminology
Index of Algorithms
Basic constructions
On nilpotency and colvability
Cartan subalgebras
4.

図書

図書
E.B. Dynkin ; A.A. Yushkevich, G.M. Seitz, A.L. Onishchik, editors
出版情報: Providence, R.I. : American Mathematical Society , Cambridge, Mass. : International Press, c2000  xxvi, 798 p. ; 27 cm
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Lie groups and Lie algebras: Dynkin and Lie theory / G. M. SeitzPart I:
On the work of E. B. Dynkin in the theory of Lie groups / F. I. Karpelevich ; A. L. Onishchik ; E. B. Vinberg
Correction to On the work of E. B. Dynkin in the theory of Lie groups
Classification of simple Lie groups / E. B. Dynkin
Calculation of the coefficients in the Campbell-Hausdorff formula
The maximal subgroups of the classical groups
Comments on Maximal subgroups of the classical groups
Semisimple subalgebras of semisimple Lie algebras
Comments on the paper Semisimple subalgebras of semisimple Lie algebras
Construction of primitive cycles in compact Lie groups
Topological characteristics of homomorphisms of compact Lie groups
Comments on the paper Topological characteristics of homomorphisms of compact Lie groups
Dynkin and modern Lie theory / B. Kostant
Comments on the impact of Dynkin's work on current research in representation theory / D. A. Vogan
Coxeter-Dynkin diagrams and singularities / A. Gabrielov
Lie groups in physics / K. Gottfried
Dynkin diagrams in the physics of particles, fields and strings / Y. Ne'eman
Probability theory: Dynkin and probability theory / A. A. YushkevichPart II:
Necessary and sufficient statistics for a family of probability distributions
Some limit theorems for sums of independent random variables with infinite mathematical expectations
Markov processes and semigroups of operators
Strong Markov processes
Infinitesimal operators of Markov processes
The natural topology and excessive functions connected with a Markov process
Random walk on groups with a finite number of generators / M. B. Malyutov
The optimum choice of the instant for stopping a Markov process
Brownian motion in certain symmetric spaces and nonnegative eigenfunctions of the Laplace-Beltrami operator
Diffusion of tensors
Game variant of a problem on optimal stopping
Determining functions of Markov processes and corresponding dual regular classes / S. E. Kuznetsov
Economic equilibrium under uncertainty
Comments on Economic equilibrium under uncertainty / I. V. Evstigneev
Markov processes and random fields
Green's and Dirichlet spaces associated with fine Markov processes
Markov processes as a tool in field theory
Symmetric statistics, Poisson point processes, and multiple Wiener integrals / A. Mandelbaum
Gaussian and non-Gaussian random fields associated with Markov processes
Author's correction to Guassian and non-Gaussian random fields associated with Markov processes.
An application of flows to time shift and time reversal in stochastic processes
Author's comments on An application of flows to time shift and time reversal in stochastic processes
Representation for functionals of superprocesses by multiple stochastic integrals, with applications to self-intersection local times
A probabilistic approach to one class of nonlinear differential equations
Superdiffusions and parabolic nonlinear differential equations
Comments on Superdiffusions and parabolic nonlinear differential equations
Dynkin and the theory of Markov processes / P. A. Meyer
To the history of strong Markov property
On compactifications of symmetric spaces / M. A. Olshanetsky
Dynkin's contributions to superprocesses and partial differential equations / J.-F. Le Gall
Dynkin's work in mathematical economics
Acknowledgments
Lie groups and Lie algebras: Dynkin and Lie theory / G. M. SeitzPart I:
On the work of E. B. Dynkin in the theory of Lie groups / F. I. Karpelevich ; A. L. Onishchik ; E. B. Vinberg
Correction to On the work of E. B. Dynkin in the theory of Lie groups
5.

図書

図書
A.L. Onishchik, E.B. Vinberg (eds.)
出版情報: Berlin : Springer, c2000  223 p. ; 24 cm
シリーズ名: Encyclopaedia of mathematical sciences / editor-in-chief, R.V. Gamkrelidze ; v. 21 . Lie groups and Lie algebras ; 2
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6.

図書

図書
Minoru Wakimoto ; translated by Kenji Iohara
出版情報: Providence, RI : American Mathematical Society, c2001  xviii, 304 p. ; 22 cm
シリーズ名: Iwanami series in modern mathematics
Translations of mathematical monographs ; v. 195
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Opening Structures and representations of BKM (super-)algebras
Affine Lie algebras Modular transformations of characters of affine Lie algebras
Fusion algebras In lieu of postscript-Virasoro algebra
Further developments
Bibliography
Index
Opening Structures and representations of BKM (super-)algebras
Affine Lie algebras Modular transformations of characters of affine Lie algebras
Fusion algebras In lieu of postscript-Virasoro algebra
7.

図書

図書
by Constantin Vârsan
出版情報: Dordrecht ; Boston : Kluwer Academic Publishers, c1999  x, 238 p. ; 25 cm
シリーズ名: Mathematics and its applications ; v. 466
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8.

図書

図書
by Antonio Kumpera and Donald Spencer
出版情報: Princeton, N.J. : Princeton University Press , Tokyo : University of Tokyo Press, 1972  xv, 293 p. ; 24 cm
シリーズ名: Annals of mathematics studies ; no. 73 . Lie equations / by Antonio Kumpera and Donald Spencer ; v. 1
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9.

図書

図書
Wolfgang Bertram
出版情報: Berlin : Springer, c2000  xvi, 269 p. ; 24 cm
シリーズ名: Lecture notes in mathematics ; 1754
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10.

図書

図書
Jean-Pierre Serre ; translated from the French by G.A. Jones
出版情報: New York : Springer, 2001  ix, 74 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
Nilpotent Lie Algebras and Solvable Lie Algebras
Semisimple Lie Algebras (General Theorems)
Cartan Subalgebras
The Algebra sl2 and Its Representations
Root Systems
Structure of Semisimple Lie Algebras
Linear Representations of Semisimple Lie Algebras
Complex Groups and Compact groups
Bibliography
Index
Nilpotent Lie Algebras and Solvable Lie Algebras
Semisimple Lie Algebras (General Theorems)
Cartan Subalgebras
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