Notes on Lie Algebras:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1990
|
| Schriftenreihe: | Universitext
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | (Cartan sub Lie algebra, roots, Weyl group, Dynkin diagram, . . . ) and the classification, as found by Killing and Cartan (the list of all semisimple Lie algebras consists of (1) the special- linear ones, i. e. all matrices (of any fixed dimension) with trace 0, (2) the orthogonal ones, i. e. all skewsymmetric ma trices (of any fixed dimension), (3) the symplectic ones, i. e. all matrices M (of any fixed even dimension) that satisfy M J = - J MT with a certain non-degenerate skewsymmetric matrix J, and (4) five special Lie algebras G2, F , E , E , E , of dimensions 14,52,78,133,248, the "exceptional Lie 4 6 7 s algebras" , that just somehow appear in the process). There is also a discus sion of the compact form and other real forms of a (complex) semisimple Lie algebra, and a section on automorphisms. The third chapter brings the theory of the finite dimensional representations of a semisimple Lie alge bra, with the highest or extreme weight as central notion. The proof for the existence of representations is an ad hoc version of the present standard proof, but avoids explicit use of the Poincare-Birkhoff-Witt theorem. Complete reducibility is proved, as usual, with J. H. C. Whitehead's proof (the first proof, by H. Weyl, was analytical-topological and used the exis tence of a compact form of the group in question). Then come H. |
| Beschreibung: | 1 Online-Ressource (XII, 162p. 5 illus) |
| ISBN: | 9781461390145 9780387972640 |
| ISSN: | 0172-5939 |
| DOI: | 10.1007/978-1-4613-9014-5 |
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Datensatz im Suchindex
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| author | Samelson, Hans |
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| author_sort | Samelson, Hans |
| author_variant | h s hs |
| building | Verbundindex |
| bvnumber | BV042420760 |
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| ctrlnum | (OCoLC)863792422 (DE-599)BVBBV042420760 |
| dewey-full | 512.482 512.55 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.482 512.55 |
| dewey-search | 512.482 512.55 |
| dewey-sort | 3512.482 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4613-9014-5 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:07Z |
| institution | BVB |
| isbn | 9781461390145 9780387972640 |
| issn | 0172-5939 |
| language | English |
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| physical | 1 Online-Ressource (XII, 162p. 5 illus) |
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| publisher | Springer New York |
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| spelling | Samelson, Hans Verfasser aut Notes on Lie Algebras by Hans Samelson New York, NY Springer New York 1990 1 Online-Ressource (XII, 162p. 5 illus) txt rdacontent c rdamedia cr rdacarrier Universitext 0172-5939 (Cartan sub Lie algebra, roots, Weyl group, Dynkin diagram, . . . ) and the classification, as found by Killing and Cartan (the list of all semisimple Lie algebras consists of (1) the special- linear ones, i. e. all matrices (of any fixed dimension) with trace 0, (2) the orthogonal ones, i. e. all skewsymmetric ma trices (of any fixed dimension), (3) the symplectic ones, i. e. all matrices M (of any fixed even dimension) that satisfy M J = - J MT with a certain non-degenerate skewsymmetric matrix J, and (4) five special Lie algebras G2, F , E , E , E , of dimensions 14,52,78,133,248, the "exceptional Lie 4 6 7 s algebras" , that just somehow appear in the process). There is also a discus sion of the compact form and other real forms of a (complex) semisimple Lie algebra, and a section on automorphisms. The third chapter brings the theory of the finite dimensional representations of a semisimple Lie alge bra, with the highest or extreme weight as central notion. The proof for the existence of representations is an ad hoc version of the present standard proof, but avoids explicit use of the Poincare-Birkhoff-Witt theorem. Complete reducibility is proved, as usual, with J. H. C. Whitehead's proof (the first proof, by H. Weyl, was analytical-topological and used the exis tence of a compact form of the group in question). Then come H. Mathematics Topological Groups Topological Groups, Lie Groups Mathematik Lie-Algebra (DE-588)4130355-6 gnd rswk-swf Lie-Algebra (DE-588)4130355-6 s 1\p DE-604 https://doi.org/10.1007/978-1-4613-9014-5 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Samelson, Hans Notes on Lie Algebras Mathematics Topological Groups Topological Groups, Lie Groups Mathematik Lie-Algebra (DE-588)4130355-6 gnd |
| subject_GND | (DE-588)4130355-6 |
| title | Notes on Lie Algebras |
| title_auth | Notes on Lie Algebras |
| title_exact_search | Notes on Lie Algebras |
| title_full | Notes on Lie Algebras by Hans Samelson |
| title_fullStr | Notes on Lie Algebras by Hans Samelson |
| title_full_unstemmed | Notes on Lie Algebras by Hans Samelson |
| title_short | Notes on Lie Algebras |
| title_sort | notes on lie algebras |
| topic | Mathematics Topological Groups Topological Groups, Lie Groups Mathematik Lie-Algebra (DE-588)4130355-6 gnd |
| topic_facet | Mathematics Topological Groups Topological Groups, Lie Groups Mathematik Lie-Algebra |
| url | https://doi.org/10.1007/978-1-4613-9014-5 |
| work_keys_str_mv | AT samelsonhans notesonliealgebras |