Quantum Groups and Their Primitive Ideals:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1995
|
| Schriftenreihe: | Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge A Series of Modern Surveys in Mathematics
29 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | by a more general quadratic algebra (possibly obtained by deformation) and then to derive Rq [G] by requiring it to possess the latter as a comodule. A third principle is to focus attention on the tensor structure of the cat egory of (!; modules. This means of course just defining an algebra structure on Rq[G]; but this is to be done in a very specific manner. Concretely the category is required to be braided and this forces (9.4.2) the existence of an "R-matrix" satisfying in particular the quantum Yang-Baxter equation and from which the algebra structure of Rq[G] can be written down (9.4.5). Finally there was a search for a perfectly self-dual model for Rq[G] which would then be isomorphic to Uq(g). Apparently this failed; but V. G. Drinfeld found that it could be essentially made to work for the "Borel part" of Uq(g) denoted U (b) and further found a general construction (the Drinfeld double) q mirroring a Lie bialgebra. This gives Uq(g) up to passage to a quotient. One of the most remarkable aspects of the above superficially different ap proaches is their extraordinary intercoherence. In particular they essentially all lead for G semisimple to the same and hence "canonical", objects Rq[G] and Uq(g), though this epithet may as yet be premature |
| Beschreibung: | 1 Online-Ressource (IX, 383p. 2 illus) |
| ISBN: | 9783642784002 9783642784026 |
| ISSN: | 0071-1136 |
| DOI: | 10.1007/978-3-642-78400-2 |
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Datensatz im Suchindex
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| any_adam_object | |
| author | Joseph, Anthony |
| author_facet | Joseph, Anthony |
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| author_sort | Joseph, Anthony |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-78400-2 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:12Z |
| institution | BVB |
| isbn | 9783642784002 9783642784026 |
| issn | 0071-1136 |
| language | English |
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| physical | 1 Online-Ressource (IX, 383p. 2 illus) |
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| publishDate | 1995 |
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| series2 | Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge A Series of Modern Surveys in Mathematics |
| spelling | Joseph, Anthony Verfasser aut Quantum Groups and Their Primitive Ideals by Anthony Joseph Berlin, Heidelberg Springer Berlin Heidelberg 1995 1 Online-Ressource (IX, 383p. 2 illus) txt rdacontent c rdamedia cr rdacarrier Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge A Series of Modern Surveys in Mathematics 29 0071-1136 by a more general quadratic algebra (possibly obtained by deformation) and then to derive Rq [G] by requiring it to possess the latter as a comodule. A third principle is to focus attention on the tensor structure of the cat egory of (!; modules. This means of course just defining an algebra structure on Rq[G]; but this is to be done in a very specific manner. Concretely the category is required to be braided and this forces (9.4.2) the existence of an "R-matrix" satisfying in particular the quantum Yang-Baxter equation and from which the algebra structure of Rq[G] can be written down (9.4.5). Finally there was a search for a perfectly self-dual model for Rq[G] which would then be isomorphic to Uq(g). Apparently this failed; but V. G. Drinfeld found that it could be essentially made to work for the "Borel part" of Uq(g) denoted U (b) and further found a general construction (the Drinfeld double) q mirroring a Lie bialgebra. This gives Uq(g) up to passage to a quotient. One of the most remarkable aspects of the above superficially different ap proaches is their extraordinary intercoherence. In particular they essentially all lead for G semisimple to the same and hence "canonical", objects Rq[G] and Uq(g), though this epithet may as yet be premature Mathematics Geometry, algebraic Algebra Topological Groups Non-associative Rings and Algebras Associative Rings and Algebras Topological Groups, Lie Groups Algebraic Geometry Theoretical, Mathematical and Computational Physics Mathematik Quantengruppe (DE-588)4252437-4 gnd rswk-swf Primitives Ideal (DE-588)4261523-9 gnd rswk-swf Hopf-Algebra (DE-588)4160646-2 gnd rswk-swf Quantengruppe (DE-588)4252437-4 s Primitives Ideal (DE-588)4261523-9 s 1\p DE-604 Hopf-Algebra (DE-588)4160646-2 s 2\p DE-604 https://doi.org/10.1007/978-3-642-78400-2 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Joseph, Anthony Quantum Groups and Their Primitive Ideals Mathematics Geometry, algebraic Algebra Topological Groups Non-associative Rings and Algebras Associative Rings and Algebras Topological Groups, Lie Groups Algebraic Geometry Theoretical, Mathematical and Computational Physics Mathematik Quantengruppe (DE-588)4252437-4 gnd Primitives Ideal (DE-588)4261523-9 gnd Hopf-Algebra (DE-588)4160646-2 gnd |
| subject_GND | (DE-588)4252437-4 (DE-588)4261523-9 (DE-588)4160646-2 |
| title | Quantum Groups and Their Primitive Ideals |
| title_auth | Quantum Groups and Their Primitive Ideals |
| title_exact_search | Quantum Groups and Their Primitive Ideals |
| title_full | Quantum Groups and Their Primitive Ideals by Anthony Joseph |
| title_fullStr | Quantum Groups and Their Primitive Ideals by Anthony Joseph |
| title_full_unstemmed | Quantum Groups and Their Primitive Ideals by Anthony Joseph |
| title_short | Quantum Groups and Their Primitive Ideals |
| title_sort | quantum groups and their primitive ideals |
| topic | Mathematics Geometry, algebraic Algebra Topological Groups Non-associative Rings and Algebras Associative Rings and Algebras Topological Groups, Lie Groups Algebraic Geometry Theoretical, Mathematical and Computational Physics Mathematik Quantengruppe (DE-588)4252437-4 gnd Primitives Ideal (DE-588)4261523-9 gnd Hopf-Algebra (DE-588)4160646-2 gnd |
| topic_facet | Mathematics Geometry, algebraic Algebra Topological Groups Non-associative Rings and Algebras Associative Rings and Algebras Topological Groups, Lie Groups Algebraic Geometry Theoretical, Mathematical and Computational Physics Mathematik Quantengruppe Primitives Ideal Hopf-Algebra |
| url | https://doi.org/10.1007/978-3-642-78400-2 |
| work_keys_str_mv | AT josephanthony quantumgroupsandtheirprimitiveideals |