Hopf algebras and root systems:
This book is an introduction to Hopf algebras in braided monoidal categories with applications to Hopf algebras in the usual sense. The main goal of the book is to present from scratch and with complete proofs the theory of Nichols algebras (or quantum symmetric algebras) and the surprising relation...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
[2020]
|
| Schriftenreihe: | Mathematical surveys and monographs
Volume 247 |
| Schlagworte: | |
| Zusammenfassung: | This book is an introduction to Hopf algebras in braided monoidal categories with applications to Hopf algebras in the usual sense. The main goal of the book is to present from scratch and with complete proofs the theory of Nichols algebras (or quantum symmetric algebras) and the surprising relationship between Nichols algebras and generalized root systems. In general, Nichols algebras are not classified by Cartan graphs and their root systems. However, extending partial results in the literature, the authors were able to associate a Cartan graph to a large class of Nichols algebras. This allows them to determine the structure of right coideal subalgebras of Nichols systems which generalize Nichols algebras. As applications of these results, the book contains a classification of right coideal subalgebras of quantum groups and of the small quantum groups, and a proof of the existence of PBW-bases that does not involve case by case considerations. The authors also include short chapter summaries at the beginning of each chapter and historical notes at the end of each chapter. The theory of Cartan graphs, Weyl groupoids, and generalized root systems appears here for the first time in a book form. Hence, the book serves as an introduction to the modern classification theory of pointed Hopf algebras |
| Beschreibung: | xix, 582 Seiten 27 cm |
| ISBN: | 9781470452322 1470452324 |
Internformat
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| 100 | 1 | |a Heckenberger, István |d 1969- |e Verfasser |0 (DE-588)120760754 |4 aut | |
| 245 | 1 | 0 | |a Hopf algebras and root systems |c István Heckenberger, Hans-Jürgen Schneider |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c [2020] | |
| 300 | |a xix, 582 Seiten |c 27 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematical surveys and monographs |v Volume 247 | |
| 505 | 8 | |a A quick introduction to Nichols algebras -- Basic Hopf algebra theory -- Braided monoidal categories -- Yetter-Drinfeld modules over Hopf algebras -- Gradings and filtrations -- Braided structures -- Nichols algebras -- Quantized enveloping algebras and generalizations -- Cartan graphs and Weyl groupoids -- The structure of Cartan graphs and root systems -- Cartan graphs of Lie superalgebras -- A braided monoidal isomorphism of Yetter-Drinfeld modules -- Nichols systems, and semi-Cartan graph of Nichols algebras -- Right coideal subalgebras of Nichols systems, and Cartan graph of Nichols algebras -- Nichols algebras of diagonal type -- Nichols algebras of Cartan type -- Nichols algebras over non-abelian groups | |
| 520 | 3 | |a This book is an introduction to Hopf algebras in braided monoidal categories with applications to Hopf algebras in the usual sense. The main goal of the book is to present from scratch and with complete proofs the theory of Nichols algebras (or quantum symmetric algebras) and the surprising relationship between Nichols algebras and generalized root systems. In general, Nichols algebras are not classified by Cartan graphs and their root systems. However, extending partial results in the literature, the authors were able to associate a Cartan graph to a large class of Nichols algebras. This allows them to determine the structure of right coideal subalgebras of Nichols systems which generalize Nichols algebras. As applications of these results, the book contains a classification of right coideal subalgebras of quantum groups and of the small quantum groups, and a proof of the existence of PBW-bases that does not involve case by case considerations. The authors also include short chapter summaries at the beginning of each chapter and historical notes at the end of each chapter. The theory of Cartan graphs, Weyl groupoids, and generalized root systems appears here for the first time in a book form. Hence, the book serves as an introduction to the modern classification theory of pointed Hopf algebras | |
| 650 | 0 | 7 | |a Hopf-Algebra |0 (DE-588)4160646-2 |2 gnd |9 rswk-swf |
| 653 | 0 | |a Hopf algebras | |
| 653 | 0 | |a Root systems (Algebra) | |
| 653 | 0 | |a Weyl groups | |
| 653 | 0 | |a Hopf algebras | |
| 653 | 0 | |a Root systems (Algebra) | |
| 653 | 0 | |a Associative rings and algebras {For the commutative case, see 13-XX} -- Hopf algebras, quantum groups and related topics | |
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| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Schneider, Hans-Jürgen |d 1944- |0 (DE-588)13818769X |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-1-4704-5680-1 |
| 830 | 0 | |a Mathematical surveys and monographs |v Volume 247 |w (DE-604)BV000018014 |9 247 | |
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Datensatz im Suchindex
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| author | Heckenberger, István 1969- Schneider, Hans-Jürgen 1944- |
| author_GND | (DE-588)120760754 (DE-588)13818769X |
| author_facet | Heckenberger, István 1969- Schneider, Hans-Jürgen 1944- |
| author_role | aut aut |
| author_sort | Heckenberger, István 1969- |
| author_variant | i h ih h j s hjs |
| building | Verbundindex |
| bvnumber | BV046888159 |
| classification_rvk | SK 230 |
| contents | A quick introduction to Nichols algebras -- Basic Hopf algebra theory -- Braided monoidal categories -- Yetter-Drinfeld modules over Hopf algebras -- Gradings and filtrations -- Braided structures -- Nichols algebras -- Quantized enveloping algebras and generalizations -- Cartan graphs and Weyl groupoids -- The structure of Cartan graphs and root systems -- Cartan graphs of Lie superalgebras -- A braided monoidal isomorphism of Yetter-Drinfeld modules -- Nichols systems, and semi-Cartan graph of Nichols algebras -- Right coideal subalgebras of Nichols systems, and Cartan graph of Nichols algebras -- Nichols algebras of diagonal type -- Nichols algebras of Cartan type -- Nichols algebras over non-abelian groups |
| ctrlnum | (OCoLC)1199061081 (DE-599)BVBBV046888159 |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| id | DE-604.BV046888159 |
| illustrated | Not Illustrated |
| index_date | 2024-07-03T15:20:11Z |
| indexdate | 2024-07-10T08:56:38Z |
| institution | BVB |
| isbn | 9781470452322 1470452324 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-032298052 |
| oclc_num | 1199061081 |
| open_access_boolean | |
| owner | DE-20 DE-19 DE-BY-UBM |
| owner_facet | DE-20 DE-19 DE-BY-UBM |
| physical | xix, 582 Seiten 27 cm |
| publishDate | 2020 |
| publishDateSearch | 2020 |
| publishDateSort | 2020 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Mathematical surveys and monographs |
| series2 | Mathematical surveys and monographs |
| spelling | Heckenberger, István 1969- Verfasser (DE-588)120760754 aut Hopf algebras and root systems István Heckenberger, Hans-Jürgen Schneider Providence, Rhode Island American Mathematical Society [2020] xix, 582 Seiten 27 cm txt rdacontent n rdamedia nc rdacarrier Mathematical surveys and monographs Volume 247 A quick introduction to Nichols algebras -- Basic Hopf algebra theory -- Braided monoidal categories -- Yetter-Drinfeld modules over Hopf algebras -- Gradings and filtrations -- Braided structures -- Nichols algebras -- Quantized enveloping algebras and generalizations -- Cartan graphs and Weyl groupoids -- The structure of Cartan graphs and root systems -- Cartan graphs of Lie superalgebras -- A braided monoidal isomorphism of Yetter-Drinfeld modules -- Nichols systems, and semi-Cartan graph of Nichols algebras -- Right coideal subalgebras of Nichols systems, and Cartan graph of Nichols algebras -- Nichols algebras of diagonal type -- Nichols algebras of Cartan type -- Nichols algebras over non-abelian groups This book is an introduction to Hopf algebras in braided monoidal categories with applications to Hopf algebras in the usual sense. The main goal of the book is to present from scratch and with complete proofs the theory of Nichols algebras (or quantum symmetric algebras) and the surprising relationship between Nichols algebras and generalized root systems. In general, Nichols algebras are not classified by Cartan graphs and their root systems. However, extending partial results in the literature, the authors were able to associate a Cartan graph to a large class of Nichols algebras. This allows them to determine the structure of right coideal subalgebras of Nichols systems which generalize Nichols algebras. As applications of these results, the book contains a classification of right coideal subalgebras of quantum groups and of the small quantum groups, and a proof of the existence of PBW-bases that does not involve case by case considerations. The authors also include short chapter summaries at the beginning of each chapter and historical notes at the end of each chapter. The theory of Cartan graphs, Weyl groupoids, and generalized root systems appears here for the first time in a book form. Hence, the book serves as an introduction to the modern classification theory of pointed Hopf algebras Hopf-Algebra (DE-588)4160646-2 gnd rswk-swf Hopf algebras Root systems (Algebra) Weyl groups Associative rings and algebras {For the commutative case, see 13-XX} -- Hopf algebras, quantum groups and related topics Hopf-Algebra (DE-588)4160646-2 s DE-604 Schneider, Hans-Jürgen 1944- (DE-588)13818769X aut Erscheint auch als Online-Ausgabe 978-1-4704-5680-1 Mathematical surveys and monographs Volume 247 (DE-604)BV000018014 247 |
| spellingShingle | Heckenberger, István 1969- Schneider, Hans-Jürgen 1944- Hopf algebras and root systems Mathematical surveys and monographs A quick introduction to Nichols algebras -- Basic Hopf algebra theory -- Braided monoidal categories -- Yetter-Drinfeld modules over Hopf algebras -- Gradings and filtrations -- Braided structures -- Nichols algebras -- Quantized enveloping algebras and generalizations -- Cartan graphs and Weyl groupoids -- The structure of Cartan graphs and root systems -- Cartan graphs of Lie superalgebras -- A braided monoidal isomorphism of Yetter-Drinfeld modules -- Nichols systems, and semi-Cartan graph of Nichols algebras -- Right coideal subalgebras of Nichols systems, and Cartan graph of Nichols algebras -- Nichols algebras of diagonal type -- Nichols algebras of Cartan type -- Nichols algebras over non-abelian groups Hopf-Algebra (DE-588)4160646-2 gnd |
| subject_GND | (DE-588)4160646-2 |
| title | Hopf algebras and root systems |
| title_auth | Hopf algebras and root systems |
| title_exact_search | Hopf algebras and root systems |
| title_exact_search_txtP | Hopf algebras and root systems |
| title_full | Hopf algebras and root systems István Heckenberger, Hans-Jürgen Schneider |
| title_fullStr | Hopf algebras and root systems István Heckenberger, Hans-Jürgen Schneider |
| title_full_unstemmed | Hopf algebras and root systems István Heckenberger, Hans-Jürgen Schneider |
| title_short | Hopf algebras and root systems |
| title_sort | hopf algebras and root systems |
| topic | Hopf-Algebra (DE-588)4160646-2 gnd |
| topic_facet | Hopf-Algebra |
| volume_link | (DE-604)BV000018014 |
| work_keys_str_mv | AT heckenbergeristvan hopfalgebrasandrootsystems AT schneiderhansjurgen hopfalgebrasandrootsystems |