Lie Groups and Algebraic Groups:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1990
|
| Schriftenreihe: | Springer Series in Soviet Mathematics
|
| Schlagwörter: | |
| Links: | https://doi.org/10.1007/978-3-642-74334-4 |
| Beschreibung: | This book is based on the notes of the authors' seminar on algebraic and Lie groups held at the Department of Mechanics and Mathematics of Moscow University in 1967/68. Our guiding idea was to present in the most economic way the theory of semisimple Lie groups on the basis of the theory of algebraic groups. Our main sources were A. Borel's paper [34], C. ChevalIey's seminar [14], seminar "Sophus Lie" [15] and monographs by C. Chevalley [4], N. Jacobson [9] and J-P. Serre [16, 17]. In preparing this book we have completely rearranged these notes and added two new chapters: "Lie groups" and "Real semisimple Lie groups". Several traditional topics of Lie algebra theory, however, are left entirely disregarded, e.g. universal enveloping algebras, characters of linear representations and (co)homology of Lie algebras. A distinctive feature of this book is that almost all the material is presented as a sequence of problems, as it had been in the first draft of the seminar's notes. We believe that solving these problems may help the reader to feel the seminar's atmosphere and master the theory. Nevertheless, all the non-trivial ideas, and sometimes solutions, are contained in hints given at the end of each section. The proofs of certain theorems, which we consider more difficult, are given directly in the main text. The book also contains exercises, the majority of which are an essential complement to the main contents |
| Umfang: | 1 Online-Ressource (XX, 330 p) |
| ISBN: | 9783642743344 9783642743368 |
| ISSN: | 0939-1169 |
| DOI: | 10.1007/978-3-642-74334-4 |
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| 500 | |a This book is based on the notes of the authors' seminar on algebraic and Lie groups held at the Department of Mechanics and Mathematics of Moscow University in 1967/68. Our guiding idea was to present in the most economic way the theory of semisimple Lie groups on the basis of the theory of algebraic groups. Our main sources were A. Borel's paper [34], C. ChevalIey's seminar [14], seminar "Sophus Lie" [15] and monographs by C. Chevalley [4], N. Jacobson [9] and J-P. Serre [16, 17]. In preparing this book we have completely rearranged these notes and added two new chapters: "Lie groups" and "Real semisimple Lie groups". Several traditional topics of Lie algebra theory, however, are left entirely disregarded, e.g. universal enveloping algebras, characters of linear representations and (co)homology of Lie algebras. A distinctive feature of this book is that almost all the material is presented as a sequence of problems, as it had been in the first draft of the seminar's notes. We believe that solving these problems may help the reader to feel the seminar's atmosphere and master the theory. Nevertheless, all the non-trivial ideas, and sometimes solutions, are contained in hints given at the end of each section. The proofs of certain theorems, which we consider more difficult, are given directly in the main text. The book also contains exercises, the majority of which are an essential complement to the main contents | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Geometry, algebraic | |
| 650 | 4 | |a Group theory | |
| 650 | 4 | |a Topological Groups | |
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| 650 | 4 | |a Group Theory and Generalizations | |
| 650 | 4 | |a Algebraic Geometry | |
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Datensatz im Suchindex
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| _version_ | 1821931353164218368 |
| any_adam_object | |
| author | Oniščik, Arkadij L. 1933-2019 |
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| author_sort | Oniščik, Arkadij L. 1933-2019 |
| author_variant | a l o al alo |
| building | Verbundindex |
| bvnumber | BV042422971 |
| classification_tum | MAT 000 |
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| dewey-full | 512.55 512.482 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.55 512.482 |
| dewey-search | 512.55 512.482 |
| dewey-sort | 3512.55 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-74334-4 |
| format | Electronic eBook |
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| id | DE-604.BV042422971 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T17:10:47Z |
| institution | BVB |
| isbn | 9783642743344 9783642743368 |
| issn | 0939-1169 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027858388 |
| oclc_num | 879622503 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (XX, 330 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1990 |
| publishDateSearch | 1990 |
| publishDateSort | 1990 |
| publisher | Springer Berlin Heidelberg |
| record_format | marc |
| series2 | Springer Series in Soviet Mathematics |
| spellingShingle | Oniščik, Arkadij L. 1933-2019 Lie Groups and Algebraic Groups Mathematics Geometry, algebraic Group theory Topological Groups Topological Groups, Lie Groups Group Theory and Generalizations Algebraic Geometry Theoretical, Mathematical and Computational Physics Mathematik Affine algebraische Gruppe (DE-588)4141561-9 gnd Algebraische Gruppe (DE-588)4001164-1 gnd Lie-Gruppe (DE-588)4035695-4 gnd Algebraische Mannigfaltigkeit (DE-588)4128509-8 gnd |
| subject_GND | (DE-588)4141561-9 (DE-588)4001164-1 (DE-588)4035695-4 (DE-588)4128509-8 |
| title | Lie Groups and Algebraic Groups |
| title_auth | Lie Groups and Algebraic Groups |
| title_exact_search | Lie Groups and Algebraic Groups |
| title_full | Lie Groups and Algebraic Groups by Arkadij L. Onishchik, Ernest B. Vinberg |
| title_fullStr | Lie Groups and Algebraic Groups by Arkadij L. Onishchik, Ernest B. Vinberg |
| title_full_unstemmed | Lie Groups and Algebraic Groups by Arkadij L. Onishchik, Ernest B. Vinberg |
| title_short | Lie Groups and Algebraic Groups |
| title_sort | lie groups and algebraic groups |
| topic | Mathematics Geometry, algebraic Group theory Topological Groups Topological Groups, Lie Groups Group Theory and Generalizations Algebraic Geometry Theoretical, Mathematical and Computational Physics Mathematik Affine algebraische Gruppe (DE-588)4141561-9 gnd Algebraische Gruppe (DE-588)4001164-1 gnd Lie-Gruppe (DE-588)4035695-4 gnd Algebraische Mannigfaltigkeit (DE-588)4128509-8 gnd |
| topic_facet | Mathematics Geometry, algebraic Group theory Topological Groups Topological Groups, Lie Groups Group Theory and Generalizations Algebraic Geometry Theoretical, Mathematical and Computational Physics Mathematik Affine algebraische Gruppe Algebraische Gruppe Lie-Gruppe Algebraische Mannigfaltigkeit |
| url | https://doi.org/10.1007/978-3-642-74334-4 |
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