A quantum groups primer:
This book provides a self-contained introduction to quantum groups as algebraic objects. Based on the author's lecture notes from a Part III pure mathematics course at Cambridge University, it is suitable for use as a textbook for graduate courses in quantum groups or as a supplement to modern...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2002
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| Schriftenreihe: | London Mathematical Society lecture note series
292 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 Volltext |
| Zusammenfassung: | This book provides a self-contained introduction to quantum groups as algebraic objects. Based on the author's lecture notes from a Part III pure mathematics course at Cambridge University, it is suitable for use as a textbook for graduate courses in quantum groups or as a supplement to modern courses in advanced algebra. The book assumes a background knowledge of basic algebra and linear algebra. Some familiarity with semisimple Lie algebras would also be helpful. The book is aimed as a primer for mathematicians and takes a modern approach leading into knot theory, braided categories and noncommutative differential geometry. It should also be useful for mathematical physicists |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 online resource (x, 169 pages) |
| ISBN: | 9780511549892 |
| DOI: | 10.1017/CBO9780511549892 |
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| 505 | 8 | |a Coalgebras, bialgebras and Hopf algebras. Uq(b+) -- Dual pairing. SLq(2). Actions -- Coactions. Quantum plane A2q -- Automorphism quantum groups -- Quasitriangular structures -- Roots of Unity. uq(sl2) -- q-Binomials -- Quantum double. Dual-quasitriangular structures -- Braided categories -- (Co)module categories. Crossed modules -- q-Hecke algebras -- Rigid objects. Dual representations. Quantum dimension -- Knot invariants -- Hopf algebras in braided categories -- Braided differentiation -- Bosonisation. Inhomogeneous quantum groups -- Double bosonisation. Diagrammatic construction of uq(sl2) -- The braided group Uq(n- ). Construction of Uq(g) -- q-Serre relations -- R-matrix methods -- Group algebra, Hopf algebra factorisations. Bicrossproducts -- Lie bialgebras. Lie splittings. Iwasawa decomposition -- Poisson geometry. Noncommutative bundles. q-Sphere -- Connections. q-Monopole. Nonuniversal differentials | |
| 520 | |a This book provides a self-contained introduction to quantum groups as algebraic objects. Based on the author's lecture notes from a Part III pure mathematics course at Cambridge University, it is suitable for use as a textbook for graduate courses in quantum groups or as a supplement to modern courses in advanced algebra. The book assumes a background knowledge of basic algebra and linear algebra. Some familiarity with semisimple Lie algebras would also be helpful. The book is aimed as a primer for mathematicians and takes a modern approach leading into knot theory, braided categories and noncommutative differential geometry. It should also be useful for mathematical physicists | ||
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Datensatz im Suchindex
| _version_ | 1804176884790984704 |
|---|---|
| any_adam_object | |
| author | Majid, Shahn |
| author_facet | Majid, Shahn |
| author_role | aut |
| author_sort | Majid, Shahn |
| author_variant | s m sm |
| building | Verbundindex |
| bvnumber | BV043942224 |
| classification_rvk | SI 320 SK 230 |
| collection | ZDB-20-CBO |
| contents | Coalgebras, bialgebras and Hopf algebras. Uq(b+) -- Dual pairing. SLq(2). Actions -- Coactions. Quantum plane A2q -- Automorphism quantum groups -- Quasitriangular structures -- Roots of Unity. uq(sl2) -- q-Binomials -- Quantum double. Dual-quasitriangular structures -- Braided categories -- (Co)module categories. Crossed modules -- q-Hecke algebras -- Rigid objects. Dual representations. Quantum dimension -- Knot invariants -- Hopf algebras in braided categories -- Braided differentiation -- Bosonisation. Inhomogeneous quantum groups -- Double bosonisation. Diagrammatic construction of uq(sl2) -- The braided group Uq(n- ). Construction of Uq(g) -- q-Serre relations -- R-matrix methods -- Group algebra, Hopf algebra factorisations. Bicrossproducts -- Lie bialgebras. Lie splittings. Iwasawa decomposition -- Poisson geometry. Noncommutative bundles. q-Sphere -- Connections. q-Monopole. Nonuniversal differentials |
| ctrlnum | (ZDB-20-CBO)CR9780511549892 (OCoLC)847068557 (DE-599)BVBBV043942224 |
| dewey-full | 530.14/3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.14/3 |
| dewey-search | 530.14/3 |
| dewey-sort | 3530.14 13 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| doi_str_mv | 10.1017/CBO9780511549892 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:17Z |
| institution | BVB |
| isbn | 9780511549892 |
| language | English |
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| spelling | Majid, Shahn Verfasser aut A quantum groups primer Shahn Majid Cambridge Cambridge University Press 2002 1 online resource (x, 169 pages) txt rdacontent c rdamedia cr rdacarrier London Mathematical Society lecture note series 292 Title from publisher's bibliographic system (viewed on 05 Oct 2015) Coalgebras, bialgebras and Hopf algebras. Uq(b+) -- Dual pairing. SLq(2). Actions -- Coactions. Quantum plane A2q -- Automorphism quantum groups -- Quasitriangular structures -- Roots of Unity. uq(sl2) -- q-Binomials -- Quantum double. Dual-quasitriangular structures -- Braided categories -- (Co)module categories. Crossed modules -- q-Hecke algebras -- Rigid objects. Dual representations. Quantum dimension -- Knot invariants -- Hopf algebras in braided categories -- Braided differentiation -- Bosonisation. Inhomogeneous quantum groups -- Double bosonisation. Diagrammatic construction of uq(sl2) -- The braided group Uq(n- ). Construction of Uq(g) -- q-Serre relations -- R-matrix methods -- Group algebra, Hopf algebra factorisations. Bicrossproducts -- Lie bialgebras. Lie splittings. Iwasawa decomposition -- Poisson geometry. Noncommutative bundles. q-Sphere -- Connections. q-Monopole. Nonuniversal differentials This book provides a self-contained introduction to quantum groups as algebraic objects. Based on the author's lecture notes from a Part III pure mathematics course at Cambridge University, it is suitable for use as a textbook for graduate courses in quantum groups or as a supplement to modern courses in advanced algebra. The book assumes a background knowledge of basic algebra and linear algebra. Some familiarity with semisimple Lie algebras would also be helpful. The book is aimed as a primer for mathematicians and takes a modern approach leading into knot theory, braided categories and noncommutative differential geometry. It should also be useful for mathematical physicists Quantum groups Quantengruppe (DE-588)4252437-4 gnd rswk-swf Quantengruppe (DE-588)4252437-4 s 1\p DE-604 Erscheint auch als Druckausgabe 978-0-521-01041-2 https://doi.org/10.1017/CBO9780511549892 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Majid, Shahn A quantum groups primer Coalgebras, bialgebras and Hopf algebras. Uq(b+) -- Dual pairing. SLq(2). Actions -- Coactions. Quantum plane A2q -- Automorphism quantum groups -- Quasitriangular structures -- Roots of Unity. uq(sl2) -- q-Binomials -- Quantum double. Dual-quasitriangular structures -- Braided categories -- (Co)module categories. Crossed modules -- q-Hecke algebras -- Rigid objects. Dual representations. Quantum dimension -- Knot invariants -- Hopf algebras in braided categories -- Braided differentiation -- Bosonisation. Inhomogeneous quantum groups -- Double bosonisation. Diagrammatic construction of uq(sl2) -- The braided group Uq(n- ). Construction of Uq(g) -- q-Serre relations -- R-matrix methods -- Group algebra, Hopf algebra factorisations. Bicrossproducts -- Lie bialgebras. Lie splittings. Iwasawa decomposition -- Poisson geometry. Noncommutative bundles. q-Sphere -- Connections. q-Monopole. Nonuniversal differentials Quantum groups Quantengruppe (DE-588)4252437-4 gnd |
| subject_GND | (DE-588)4252437-4 |
| title | A quantum groups primer |
| title_auth | A quantum groups primer |
| title_exact_search | A quantum groups primer |
| title_full | A quantum groups primer Shahn Majid |
| title_fullStr | A quantum groups primer Shahn Majid |
| title_full_unstemmed | A quantum groups primer Shahn Majid |
| title_short | A quantum groups primer |
| title_sort | a quantum groups primer |
| topic | Quantum groups Quantengruppe (DE-588)4252437-4 gnd |
| topic_facet | Quantum groups Quantengruppe |
| url | https://doi.org/10.1017/CBO9780511549892 |
| work_keys_str_mv | AT majidshahn aquantumgroupsprimer |