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001 978-1-4612-6398-2
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008 121227s1972 xxu| s |||| 0|eng d
020 _a9781461263982
_9978-1-4612-6398-2
024 7 _a10.1007/978-1-4612-6398-2
_2doi
050 4 _aQA150-272
072 7 _aPBF
_2bicssc
072 7 _aMAT002000
_2bisacsh
072 7 _aPBF
_2thema
082 0 4 _a512
_223
100 1 _aHumphreys, J.E.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aIntroduction to Lie Algebras and Representation Theory
_h[electronic resource] /
_cby J.E. Humphreys.
250 _a1st ed. 1972.
264 1 _aNew York, NY :
_bSpringer New York :
_bImprint: Springer,
_c1972.
300 _aXIII, 173 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aGraduate Texts in Mathematics,
_x0072-5285 ;
_v9
505 0 _aI. Basic Concepts -- 1. Definitions and first examples -- 2. Ideals and homomorphisms -- 3. Solvable and nilpotent Lie algebras -- II. Semisimple Lie Algebras -- 4. Theorems of Lie and Cartan -- 5. Killing form -- 6. Complete reducibility of representations -- 7. Representations of sl (2, F) -- 8. Root space decomposition -- III. Root Systems -- 9. Axiomatics -- 10. Simple roots and Weyl group -- 11. Classification -- 12. Construction of root systems and automorphisms -- 13. Abstract theory of weights -- IV. Isomorphism and Conjugacy Theorems -- 14. Isomorphism theorem -- 15. Cartan subalgebras -- 16. Conjugacy theorems -- V. Existence Theorem -- 17. Universal enveloping algebras -- 18. The simple algebras -- VI. Representation Theory -- 20. Weights and maximal vectors -- 21. Finite dimensional modules -- 22. Multiplicity formula -- 23. Characters -- 24. Formulas of Weyl, Kostant, and Steinberg -- VII. Chevalley Algebras and Groups -- 25. Chevalley basis of L -- 26. Kostant's Theorem -- 27. Admissible lattices -- References -- Afterword (1994) -- Index of Terminology -- Index of Symbols.
520 _aThis 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 admittedly a little more demanding. Besides being useful in many parts of mathematics and physics, the theory of semisimple Lie algebras is inherently attractive, combining as it does a certain amount of depth and a satisfying degree of completeness in its basic results. Since Jacobson's book appeared a decade ago, improvements have been made even in the classical parts of the theory. I have tried to incor­ porate some of them here and to provide easier access to the subject for non-specialists. For the specialist, the following features should be noted: (I) The Jordan-Chevalley decomposition of linear transformations is emphasized, with "toral" subalgebras replacing the more traditional Cartan subalgebras in the semisimple case. (2) The conjugacy theorem for Cartan subalgebras is proved (following D. J. Winter and G. D. Mostow) by elementary Lie algebra methods, avoiding the use of algebraic geometry.
650 0 _aAlgebra.
650 1 4 _aAlgebra.
_0https://scigraph.springernature.com/ontologies/product-market-codes/M11000
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9780387900520
776 0 8 _iPrinted edition:
_z9781489984005
776 0 8 _iPrinted edition:
_z9780387900537
776 0 8 _iPrinted edition:
_z9781461263999
830 0 _aGraduate Texts in Mathematics,
_x0072-5285 ;
_v9
856 4 0 _uhttps://doi.org/10.1007/978-1-4612-6398-2
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912 _aZDB-2-SXMS
912 _aZDB-2-BAE
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