Quadrangular Algebras:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Princeton, N.J.
Princeton University Press
2005
|
| Schriftenreihe: | Mathematical Notes
46 |
| Schlagworte: | |
| Online-Zugang: | FAB01 FAW01 FCO01 FHA01 FKE01 FLA01 UPA01 Volltext Volltext |
| Beschreibung: | Main description: This book introduces a new class of non-associative algebras related to certain exceptional algebraic groups and their associated buildings. Richard Weiss develops a theory of these "quadrangular algebras" that opens the first purely algebraic approach to the exceptional Moufang quadrangles. These quadrangles include both those that arise as the spherical buildings associated to groups of type E6, E7, and E8 as well as the exotic quadrangles "of type F4" discovered earlier by Weiss. Based on their relationship to exceptional algebraic groups, quadrangular algebras belong in a series together with alternative and Jordan division algebras. Formally, the notion of a quadrangular algebra is derived from the notion of a pseudo-quadratic space (introduced by Jacques Tits in the study of classical groups) over a quaternion division ring. This book contains the complete classification of quadrangular algebras starting from first principles. It also shows how this classification can be made to yield the classification of exceptional Moufang quadrangles as a consequence. The book closes with a chapter on isotopes and the structure group of a quadrangular algebra. Quadrangular Algebras is intended for graduate students of mathematics as well as specialists in buildings, exceptional algebraic groups, and related algebraic structures including Jordan algebras and the algebraic theory of quadratic forms |
| Beschreibung: | 1 Online-Ressource (144 S.) |
| ISBN: | 9781400826940 |
| DOI: | 10.1515/9781400826940 |
Internformat
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV042522320 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150423s2005 |||| o||u| ||||||eng d | ||
| 020 | |a 9781400826940 |9 978-1-4008-2694-0 | ||
| 024 | 7 | |a 10.1515/9781400826940 |2 doi | |
| 035 | |a (OCoLC)890450648 | ||
| 035 | |a (DE-599)BVBBV042522320 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-859 |a DE-860 |a DE-Aug4 |a DE-739 |a DE-1046 |a DE-1043 |a DE-858 | ||
| 100 | 1 | |a Weiss, Richard M. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Quadrangular Algebras |
| 264 | 1 | |a Princeton, N.J. |b Princeton University Press |c 2005 | |
| 300 | |a 1 Online-Ressource (144 S.) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Mathematical Notes |v 46 | |
| 500 | |a Main description: This book introduces a new class of non-associative algebras related to certain exceptional algebraic groups and their associated buildings. Richard Weiss develops a theory of these "quadrangular algebras" that opens the first purely algebraic approach to the exceptional Moufang quadrangles. These quadrangles include both those that arise as the spherical buildings associated to groups of type E6, E7, and E8 as well as the exotic quadrangles "of type F4" discovered earlier by Weiss. Based on their relationship to exceptional algebraic groups, quadrangular algebras belong in a series together with alternative and Jordan division algebras. Formally, the notion of a quadrangular algebra is derived from the notion of a pseudo-quadratic space (introduced by Jacques Tits in the study of classical groups) over a quaternion division ring. This book contains the complete classification of quadrangular algebras starting from first principles. It also shows how this classification can be made to yield the classification of exceptional Moufang quadrangles as a consequence. The book closes with a chapter on isotopes and the structure group of a quadrangular algebra. Quadrangular Algebras is intended for graduate students of mathematics as well as specialists in buildings, exceptional algebraic groups, and related algebraic structures including Jordan algebras and the algebraic theory of quadratic forms | ||
| 650 | 0 | 7 | |a Quadratische Form |0 (DE-588)4128297-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Algebra |0 (DE-588)4001156-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Nichtassoziative Algebra |0 (DE-588)4297760-5 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Quadratische Form |0 (DE-588)4128297-8 |D s |
| 689 | 0 | 1 | |a Algebra |0 (DE-588)4001156-2 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 689 | 1 | 0 | |a Nichtassoziative Algebra |0 (DE-588)4297760-5 |D s |
| 689 | 1 | |8 2\p |5 DE-604 | |
| 856 | 4 | 0 | |u https://doi.org/10.1515/9781400826940 |x Verlag |3 Volltext |
| 856 | 4 | 0 | |u http://www.degruyter.com/search?f_0=isbnissn&q_0=9781400826940&searchTitles=true |x Verlag |3 Volltext |
| 912 | |a ZDB-23-DGG | ||
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027956659 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 883 | 1 | |8 2\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 966 | e | |u https://doi.org/10.1515/9781400826940?locatt=mode:legacy |l FAB01 |p ZDB-23-DGG |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1515/9781400826940?locatt=mode:legacy |l FAW01 |p ZDB-23-DGG |q FAW_PDA_DGG |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1515/9781400826940?locatt=mode:legacy |l FCO01 |p ZDB-23-DGG |q FCO_PDA_DGG |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1515/9781400826940?locatt=mode:legacy |l FHA01 |p ZDB-23-DGG |q FHA_PDA_DGG |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1515/9781400826940?locatt=mode:legacy |l FKE01 |p ZDB-23-DGG |q FKE_PDA_DGG |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1515/9781400826940?locatt=mode:legacy |l FLA01 |p ZDB-23-DGG |q FLA_PDA_DGG |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1515/9781400826940?locatt=mode:legacy |l UPA01 |p ZDB-23-DGG |q UPA_PDA_DGG |x Verlag |3 Volltext | |
Datensatz im Suchindex
| _version_ | 1804153274918502400 |
|---|---|
| any_adam_object | |
| author | Weiss, Richard M. |
| author_facet | Weiss, Richard M. |
| author_role | aut |
| author_sort | Weiss, Richard M. |
| author_variant | r m w rm rmw |
| building | Verbundindex |
| bvnumber | BV042522320 |
| collection | ZDB-23-DGG |
| ctrlnum | (OCoLC)890450648 (DE-599)BVBBV042522320 |
| doi_str_mv | 10.1515/9781400826940 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03954nmm a2200529zcb4500</leader><controlfield tag="001">BV042522320</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150423s2005 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781400826940</subfield><subfield code="9">978-1-4008-2694-0</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1515/9781400826940</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)890450648</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042522320</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-859</subfield><subfield code="a">DE-860</subfield><subfield code="a">DE-Aug4</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-1046</subfield><subfield code="a">DE-1043</subfield><subfield code="a">DE-858</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Weiss, Richard M.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Quadrangular Algebras</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Princeton, N.J.</subfield><subfield code="b">Princeton University Press</subfield><subfield code="c">2005</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (144 S.)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Mathematical Notes</subfield><subfield code="v">46</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Main description: This book introduces a new class of non-associative algebras related to certain exceptional algebraic groups and their associated buildings. Richard Weiss develops a theory of these "quadrangular algebras" that opens the first purely algebraic approach to the exceptional Moufang quadrangles. These quadrangles include both those that arise as the spherical buildings associated to groups of type E6, E7, and E8 as well as the exotic quadrangles "of type F4" discovered earlier by Weiss. Based on their relationship to exceptional algebraic groups, quadrangular algebras belong in a series together with alternative and Jordan division algebras. Formally, the notion of a quadrangular algebra is derived from the notion of a pseudo-quadratic space (introduced by Jacques Tits in the study of classical groups) over a quaternion division ring. This book contains the complete classification of quadrangular algebras starting from first principles. It also shows how this classification can be made to yield the classification of exceptional Moufang quadrangles as a consequence. The book closes with a chapter on isotopes and the structure group of a quadrangular algebra. Quadrangular Algebras is intended for graduate students of mathematics as well as specialists in buildings, exceptional algebraic groups, and related algebraic structures including Jordan algebras and the algebraic theory of quadratic forms</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Quadratische Form</subfield><subfield code="0">(DE-588)4128297-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Algebra</subfield><subfield code="0">(DE-588)4001156-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Nichtassoziative Algebra</subfield><subfield code="0">(DE-588)4297760-5</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Quadratische Form</subfield><subfield code="0">(DE-588)4128297-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Algebra</subfield><subfield code="0">(DE-588)4001156-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Nichtassoziative Algebra</subfield><subfield code="0">(DE-588)4297760-5</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="8">2\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1515/9781400826940</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">http://www.degruyter.com/search?f_0=isbnissn&q_0=9781400826940&searchTitles=true</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-23-DGG</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027956659</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">2\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1515/9781400826940?locatt=mode:legacy</subfield><subfield code="l">FAB01</subfield><subfield code="p">ZDB-23-DGG</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1515/9781400826940?locatt=mode:legacy</subfield><subfield code="l">FAW01</subfield><subfield code="p">ZDB-23-DGG</subfield><subfield code="q">FAW_PDA_DGG</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1515/9781400826940?locatt=mode:legacy</subfield><subfield code="l">FCO01</subfield><subfield code="p">ZDB-23-DGG</subfield><subfield code="q">FCO_PDA_DGG</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1515/9781400826940?locatt=mode:legacy</subfield><subfield code="l">FHA01</subfield><subfield code="p">ZDB-23-DGG</subfield><subfield code="q">FHA_PDA_DGG</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1515/9781400826940?locatt=mode:legacy</subfield><subfield code="l">FKE01</subfield><subfield code="p">ZDB-23-DGG</subfield><subfield code="q">FKE_PDA_DGG</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1515/9781400826940?locatt=mode:legacy</subfield><subfield code="l">FLA01</subfield><subfield code="p">ZDB-23-DGG</subfield><subfield code="q">FLA_PDA_DGG</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1515/9781400826940?locatt=mode:legacy</subfield><subfield code="l">UPA01</subfield><subfield code="p">ZDB-23-DGG</subfield><subfield code="q">UPA_PDA_DGG</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield></record></collection> |
| id | DE-604.BV042522320 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:24:01Z |
| institution | BVB |
| isbn | 9781400826940 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027956659 |
| oclc_num | 890450648 |
| open_access_boolean | |
| owner | DE-859 DE-860 DE-Aug4 DE-739 DE-1046 DE-1043 DE-858 |
| owner_facet | DE-859 DE-860 DE-Aug4 DE-739 DE-1046 DE-1043 DE-858 |
| physical | 1 Online-Ressource (144 S.) |
| psigel | ZDB-23-DGG ZDB-23-DGG FAW_PDA_DGG ZDB-23-DGG FCO_PDA_DGG ZDB-23-DGG FHA_PDA_DGG ZDB-23-DGG FKE_PDA_DGG ZDB-23-DGG FLA_PDA_DGG ZDB-23-DGG UPA_PDA_DGG |
| publishDate | 2005 |
| publishDateSearch | 2005 |
| publishDateSort | 2005 |
| publisher | Princeton University Press |
| record_format | marc |
| series2 | Mathematical Notes |
| spelling | Weiss, Richard M. Verfasser aut Quadrangular Algebras Princeton, N.J. Princeton University Press 2005 1 Online-Ressource (144 S.) txt rdacontent c rdamedia cr rdacarrier Mathematical Notes 46 Main description: This book introduces a new class of non-associative algebras related to certain exceptional algebraic groups and their associated buildings. Richard Weiss develops a theory of these "quadrangular algebras" that opens the first purely algebraic approach to the exceptional Moufang quadrangles. These quadrangles include both those that arise as the spherical buildings associated to groups of type E6, E7, and E8 as well as the exotic quadrangles "of type F4" discovered earlier by Weiss. Based on their relationship to exceptional algebraic groups, quadrangular algebras belong in a series together with alternative and Jordan division algebras. Formally, the notion of a quadrangular algebra is derived from the notion of a pseudo-quadratic space (introduced by Jacques Tits in the study of classical groups) over a quaternion division ring. This book contains the complete classification of quadrangular algebras starting from first principles. It also shows how this classification can be made to yield the classification of exceptional Moufang quadrangles as a consequence. The book closes with a chapter on isotopes and the structure group of a quadrangular algebra. Quadrangular Algebras is intended for graduate students of mathematics as well as specialists in buildings, exceptional algebraic groups, and related algebraic structures including Jordan algebras and the algebraic theory of quadratic forms Quadratische Form (DE-588)4128297-8 gnd rswk-swf Algebra (DE-588)4001156-2 gnd rswk-swf Nichtassoziative Algebra (DE-588)4297760-5 gnd rswk-swf Quadratische Form (DE-588)4128297-8 s Algebra (DE-588)4001156-2 s 1\p DE-604 Nichtassoziative Algebra (DE-588)4297760-5 s 2\p DE-604 https://doi.org/10.1515/9781400826940 Verlag Volltext http://www.degruyter.com/search?f_0=isbnissn&q_0=9781400826940&searchTitles=true 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 | Weiss, Richard M. Quadrangular Algebras Quadratische Form (DE-588)4128297-8 gnd Algebra (DE-588)4001156-2 gnd Nichtassoziative Algebra (DE-588)4297760-5 gnd |
| subject_GND | (DE-588)4128297-8 (DE-588)4001156-2 (DE-588)4297760-5 |
| title | Quadrangular Algebras |
| title_auth | Quadrangular Algebras |
| title_exact_search | Quadrangular Algebras |
| title_full | Quadrangular Algebras |
| title_fullStr | Quadrangular Algebras |
| title_full_unstemmed | Quadrangular Algebras |
| title_short | Quadrangular Algebras |
| title_sort | quadrangular algebras |
| topic | Quadratische Form (DE-588)4128297-8 gnd Algebra (DE-588)4001156-2 gnd Nichtassoziative Algebra (DE-588)4297760-5 gnd |
| topic_facet | Quadratische Form Algebra Nichtassoziative Algebra |
| url | https://doi.org/10.1515/9781400826940 http://www.degruyter.com/search?f_0=isbnissn&q_0=9781400826940&searchTitles=true |
| work_keys_str_mv | AT weissrichardm quadrangularalgebras |