000 03782nam a2200349 i 4500
008 001107r1987 gw b 001 0 eng
010 _a00053835
020 _a3540678271
_qalk. paper
040 _aDLC
_cDLC
_dOHX
_dC#P
_dCIN
_dBAUN
041 1 _aeng
_hfre
049 _aBAUN_MERKEZ
050 0 4 _aQA252.3
_b.S48 1987
082 0 0 _221
100 1 _aSerre, Jean Pierre
240 1 0 _aAlgèbres de Lie semi-simples complexes.
_lEnglish
245 1 0 _aComplex semisimple Lie algebras /
_cJean-Pierre Serre ; translated from the French by G.A. Jones
264 1 _aBerlin ;
_aNew York :
_bSpringer,
_c[2001]
264 4 _c©2001
300 _aix, 74 pages ;
_c24 cm
336 _atext
_btxt
_2rdacontent
337 _aunmediated
_bn
_2rdamedia
338 _avolume
_bnc
_2rdacarrier
490 1 _aSpringer monographs in mathematics,
_x1439-7382
500 _a"Reprint of the 1987 edition."
504 _aIncludes bibliographical references (pages [72]) and index
505 0 0 _tContents
_tCh. I. Nilpotent Lie Algebras and Solvable Lie Algebras.
_t1. Lower Central Series.
_t2. Definition of Nilpotent Lie Algebras.
_t3. An Example of a Nilpotent Algebra.
_t4. Engel's Theorems.
_t5. Derived Series.
_t6. Definition of Solvable Lie Algebras.
_t7. Lie's Theorem.
_t8. Cartan's Criterion.
_tCh. II. Semisimple Lie Algebras (General Theorems).
_t1. Radical and Semisimplicity.
_t2. The Cartan-Killing Criterion.
_t3. Decomposition of Semisimple Lie Algebras.
_t4. Derivations of Semisimple Lie Algebras.
_t5. Semisimple Elements and Nilpotent Elements.
_t6. Complete Reducibility Theorem.
_t7. Complex Simple Lie Algebras.
_t8. The Passage from Real to Complex.
_tCh. III. Cartan Subalgebras.
_t1. Definition of Cartan Subalgebras.
_t2. Regular Elements: Rank.
_t3. The Cartan Subalgebra Associated with a Regular Element.
_t4. Conjugacy of Cartan Subalgebras.
_t5. The Semisimple Case.
_t6. Real Lie Algebras.
_tCh. IV. The Algebra sl[subscript 2] and Its Representations.
_t1. The Lie Algebra sl[subscript 2].
_t2. Modules, Weights, Primitive Elements.
_t3. Structure of the Submodule Generated by a Primitive Elements.
_t4. The Modules W.
_t5. Structure of the Finite-Dimensional g-Modules.
_t6. Topological Properties of the Group SL[subscript 2].
_t7. Applications.
_tCh. V. Root Systems.
_t1. Symmetries.
_t2. Definition of Root Systems.
_t3. First Examples.
_t4. The Weyl Group.
_t5. Invariant Quadratic Forms.
_t6. Inverse Systems.
_t7. Relative Position of Two Roots.
_t8. Bases.
_t9. Some Properties of Bases.
_t10. Relations with the Weyl Group.
_t11. The Cartan Matrix.
_t12. The Coxeter Graph.
_t13. Irreducible Root Systems.
_t14. Classification of Connected Coxeter Graphs.
_t15. Dynkin Diagrams.
_t16. Construction of Irreducible Root Systems.
_t17. Complex Root Systems.
_tCh. VI. Structure of Semisimple Lie Algebras.
_t1. Decomposition of g.
_t2. Proof of Theorem 2.
_t3. Borel Subalgebras.
_t4. Weyl Bases.
_t5. Existence and Uniqueness Theorems.
_t6. Chevalley's Normalization. Appendix. Construction of Semisimple Lie Algebras by Generators and Relations.
_tCh. VII. Linear Representations of Semisimple Lie Algebras.
_t1. Weights.
_t2. Primitive Elements.
_t3. Irreducible Modules with a Highest Weight.
_t4. Finite-Dimensional Modules.
_t5. An Application to the Weyl Group.
_t6. Examples: sl[subscript n+1].
_t7. Characters.
_t8. H. Weyl's formula.
_tCh. VIII. Complex Group and Compact Groups.
_t1. Cartan Subgroups.
_t2. Characters.
_t3. Relations with Representations.
_t4. Borel Subgroups.
_t5. Construction of Irreducible Representations from Borel Subgroups.
_t6. Relations with Algebraic Groups.
_t7. Relations with Compact Groups.
_tBibliography.
_tIndex.
650 0 _aLie algebras
830 0 _978475
_aSpringer monographs in mathematics,
_x1439-7382
900 _a19970
900 _bSatın
942 _2lcc
_cKT
999 _c16791
_d16791